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The graph of p(x) has degree 2 and an xintercept at (2,0) can include any graph/equation Expert Answer Previous question Next question Get more help from Chegg Solve it with our precalculus problem solver and calculatorGraph P(x)=x^24 Find the properties of the given parabola Tap for more steps Rewrite the equation in vertex form Tap for more steps Complete the square for Tap for more steps Use the form , to find the values of , , and Consider the vertex form of a parabolaP(X = 1) = 3/8 ;
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P(x)=x2+3x-4 graph-P(X = 0) = 1/8 ;P(X = 3) = 1/8 ;
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Graph P(x)=(x1)(x1)(x2) Find the point at Tap for more steps Replace the variable with in the expression Simplify the result Tap for more steps Simplify each term Tap for more steps Raising to any positive power yields Raising to any positive power yields Multiply by Multiply byArootofp(x), then (↵,0) 2 R2 is a point in the graph of p(x) These points are exactly the xintercepts of the graph of p(x) The roots of a polynomial are exactly the xintercepts of its graph 135 Examples • Below is the graph of a polynomial p(x) The graph intersects theArootofp(x), then (↵,0) 2 R2 is a point in the graph of p(x) These points are exactly the xintercepts of the graph of p(x) The roots of a polynomial are exactly the xintercepts of its graph 135 Examples • Below is the graph of a polynomial p(x) The graph intersects the
You can clickanddrag to move the graph around If you just clickandrelease (without moving), then the spot you clicked on will be the new center To reset the zoom to the original click on the Reset button Using "a" Values There is a slider with "a =" on it You can use "a" in your formula and then use the slider to change the value of "aC < 0 moves it downBased on the graph, explain why or why not Algebra I – Jan '18 33 Question 33 Score 4 The student gave a complete and correct response 33 Jim is a furniture salesman His weekly pay is $300 plus 35% of his total sales for
The graph of P touches the x axis at x = 1 and x = 1 and opens up since P(x) is positive, cutting the y axis at (0,1) See graph below e) Using the graph of P above, the range of P is given by the interval 0 , ∞) Example 3 a) Show that x = 3 is a zero of polynomial P given byFind the number of zeroes of p(x), in each case (iv) The number of times the graph touches the xaxis is 2 Therefore, the number of zeroes is 2 Ex21, 1 The graphs of y = p(x) are given in following figure, for some polynomials p(x) Find the number of zeroes of p(x), in each case (v) The number of times the graph touches the xaxis is 4Question Let P= (x,y) be a point on the graph of y=x^29 Express the distance d from P to the origin as a function of x Answer by greenestamps(8423) (Show Source) You can put this solution on YOUR website!
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Find the number of zeroes of p(x), in each case (iv) The number of times the graph touches the xaxis is 2 Therefore, the number of zeroes is 2 Ex21, 1 The graphs of y = p(x) are given in following figure, for some polynomials p(x) Find the number of zeroes of p(x), in each case (v) The number of times the graph touches the xaxis is 4Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, historyThe xintercept latexx=2/latex is the repeated solution of the equation latex{\left(x 2\right)}^{2}=0/latex The graph touches the axis at the intercept and changes direction The factor is quadratic (degree 2), so the behavior near the intercept is like that of a quadratic—it bounces off of the horizontal axis at the intercept
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Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music WolframAlpha brings expertlevel knowledge andP(X = 2) = 3/8 ;The graphs section contains commands for plotting equations and inequalities The numbers section has a percentages command for explaining the most common types of percentage problems and a section for dealing with scientific notation
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A General Note Graphical Behavior of Polynomials at xIntercepts If a polynomial contains a factor of the form latex{\left(xh\right)}^{p}/latex, the behavior near the xintercept h is determined by the power pWe say that latexx=h/latex is a zero of multiplicity p The graph of a polynomial function will touch the xaxis at zeros with even multiplicities32 The graph of the function f(x) 2ax bx c is given below f(x) x Could the factors of f(x) be (x 2) and (x 3)?The graphs section contains commands for plotting equations and inequalities The numbers section has a percentages command for explaining the most common types of percentage problems and a section for dealing with scientific notation
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P(X = 3) = 1/8 ;A General Note Graphical Behavior of Polynomials at xIntercepts If a polynomial contains a factor of the form latex{\left(xh\right)}^{p}/latex, the behavior near the xintercept h is determined by the power pWe say that latexx=h/latex is a zero of multiplicity p The graph of a polynomial function will touch the xaxis at zeros with even multiplicitiesLet us start with a function, in this case it is f(x) = x 2, but it could be anything f(x) = x 2 Here are some simple things we can do to move or scale it on the graph We can move it up or down by adding a constant to the yvalue g(x) = x 2 C Note to move the line down, we use a negative value for C C > 0 moves it up;
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The xintercept latexx=2/latex is the repeated solution of the equation latex{\left(x 2\right)}^{2}=0/latex The graph touches the axis at the intercept and changes direction The factor is quadratic (degree 2), so the behavior near the intercept is like that of a quadratic—it bounces off of the horizontal axis at the interceptLet us start with a function, in this case it is f(x) = x 2, but it could be anything f(x) = x 2 Here are some simple things we can do to move or scale it on the graph We can move it up or down by adding a constant to the yvalue g(x) = x 2 C Note to move the line down, we use a negative value for C C > 0 moves it up;Beyond simple math and grouping (like "(x2)(x4)"), there are some functions you can use as well Look below to see them all They are mostly standard functions written as you might expect You can also use "pi" and "e" as their respective constants Please note You should not use fractional exponents
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A, b, c are constants;So let's make a formula In our previous example, how can we get the values 1, 3, 3 and 1 ?Solution First graph x = y Next check a point not on the line Notice that the graph of the line contains the point (0,0), so we cannot use it as a checkpoint To determine which halfplane is the solution set use any point that is obviously not on the line x = y The point ( 2,3) is such a point Using this information, graph x y
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If you don't include an equals sign, it will assume you mean "=0" It has not been well tested, so have fun with it, but don't trust it Clickanddrag to move the graph around If you just clickandrelease (without dragging), then the spot you clicked on will be the new centerMaking a Formula Now imagine we want the chances of 5 heads in 9 tosses to list all 512 outcomes will take a long time!Making a Formula Now imagine we want the chances of 5 heads in 9 tosses to list all 512 outcomes will take a long time!
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Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, historyGraph p(x)=(x2)(x2)(x3) Find the point at Tap for more steps Replace the variable with in the expression Simplify the result Tap for more steps Simplify each term Tap for more steps Raise to the power of Raise to the power of Multiply by Multiply by Simplify by adding and subtracting Tap for more stepsTwo numbers r and s sum up to 3 exactly when the average of the two numbers is \frac{1}{2}*3 = \frac{3}{2} You can also see that the midpoint of r and s corresponds to the axis of symmetry of the parabola represented by the quadratic equation y=x^2BxC
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Graphs Solve Equations x = 2 x = 2 x = 1 x = 1 Rearrange Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation What will be the solution of inequality x^45x^24The effect of the parameters on \(y = a(x p)^2 q\) The effect of \(p\) is a horizontal shift because all points are moved the same distance in the same direction (the entire graph slides to the left or to the right) Sketch the graph of \(y = \frac{1}{2}x^2 4x \frac{7}{2}\) Determine the intercepts, turning point and the axis ofChapter 4 QUADRATICS INTRODUCTION TO QUADRATICS Objectives In this section, you will add, subtract, multiply, and graph quadratics Vocabulary The standard format of a quadratic equation is y = ax 2 bx c;
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The graph of p(x) has degree 2 and an xintercept at (2,0) can include any graph/equation Expert Answer Previous question Next question Get more help from Chegg Solve it with our precalculus problem solver and calculatorFind the number of zeroes of p(x), in each case (iv) The number of times the graph touches the xaxis is 2 Therefore, the number of zeroes is 2 Ex21, 1 The graphs of y = p(x) are given in following figure, for some polynomials p(x) Find the number of zeroes of p(x), in each case (v) The number of times the graph touches the xaxis is 4If you don't include an equals sign, it will assume you mean "=0" It has not been well tested, so have fun with it, but don't trust it Clickanddrag to move the graph around If you just clickandrelease (without dragging), then the spot you clicked on will be the new center
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Beyond simple math and grouping (like "(x2)(x4)"), there are some functions you can use as well Look below to see them all They are mostly standard functions written as you might expect You can also use "pi" and "e" as their respective constants Please note You should not use fractional exponentsTwo numbers r and s sum up to 5 exactly when the average of the two numbers is \frac{1}{2}*5 = \frac{5}{2} You can also see that the midpoint of r and s corresponds to the axis of symmetry of the parabola represented by the quadratic equation y=x^2BxCGiven random variables,, , that are defined on a probability space, the joint probability distribution for ,, is a probability distribution that gives the probability that each of ,, falls in any particular range or discrete set of values specified for that variable In the case of only two random variables, this is called a bivariate distribution, but the concept generalizes to any
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And this is what it looks like as a graph It is symmetrical!P(X = 1) = 3/8 ;The graphs section contains commands for plotting equations and inequalities The numbers section has a percentages command for explaining the most common types of percentage problems and a section for dealing with scientific notation
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A point on the graph has coordinates (x,x^29) The distance of that point from the origin (0,0) isYou can clickanddrag to move the graph around If you just clickandrelease (without moving), then the spot you clicked on will be the new center To reset the zoom to the original click on the Reset button Using "a" Values There is a slider with "a =" on it You can use "a" in your formula and then use the slider to change the value of "aFree graphing calculator instantly graphs your math problems Mathway Visit Mathway on the web Download free on Google Play Download free on iTunes Download free on Amazon Download free in Windows Store get Go Graphing Basic Math PreAlgebra Algebra Trigonometry Precalculus Calculus Statistics Finite Math Linear Algebra
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Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with stepbystep explanations, just like a math tutorGraph the parabola, y =x^21 by finding the turning point and using a table to find values for x and yThe xintercept latexx=2/latex is the repeated solution of the equation latex{\left(x 2\right)}^{2}=0/latex The graph touches the axis at the intercept and changes direction The factor is quadratic (degree 2), so the behavior near the intercept is like that of a quadratic—it bounces off of the horizontal axis at the intercept
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Let us start with a function, in this case it is f(x) = x 2, but it could be anything f(x) = x 2 Here are some simple things we can do to move or scale it on the graph We can move it up or down by adding a constant to the yvalue g(x) = x 2 C Note to move the line down, we use a negative value for C C > 0 moves it up;Sal uses the zeros of y=x^33x^2x3 to determine its corresponding graph Sal uses the zeros of y=x^33x^2x3 to determine its corresponding graph If you're seeing this message, it means we're having trouble loading external resources on our websiteX is the independent variable, and y is the dependent variableQuadratics are also called second degree polynomials because the highest exponent is 2
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So let's make a formula In our previous example, how can we get the values 1, 3, 3 and 1 ?Analyzing the Graphs of y = sec x and y = cscx The secant was defined by the reciprocal identity sec x = 1 cos x sec x = 1 cos x Notice that the function is undefined when the cosine is 0, leading to vertical asymptotes at π 2, π 2, 3 π 2, 3 π 2, etc Because the cosine is never more than 1 in absolute value, the secant, being the reciprocal, will never be less than 1 in absolute valueCompute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history
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P(X = 2) = 3/8 ;P(X = 0) = 1/8 ;C < 0 moves it down
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That is = 0 Hence we can deduce that x=1 is a zero of P(x) and (x1) a factor x^36x^211x6 = (x1)(x^25x6) Then to factor the remaining quadratic note that 5 = 23 and 6 = 2*3, and hence x^25x6 = (x2)(x3) Either way we arrive at our result x^36x^211x6 = (x1)(x2)(x3)C < 0 moves it downAnd this is what it looks like as a graph It is symmetrical!
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Analyzing the Graphs of y = sec x and y = cscx The secant was defined by the reciprocal identity sec x = 1 cos x sec x = 1 cos x Notice that the function is undefined when the cosine is 0, leading to vertical asymptotes at π 2, π 2, 3 π 2, 3 π 2, etc Because the cosine is never more than 1 in absolute value, the secant, being the reciprocal, will never be less than 1 in absolute valueGraph of the basic quadratic function f(x) = x 2 Example 1 Find points on the graph of the function f(x) = x 2 and graph it We first note that 1) because the square of real number is either positive or zero, x 2 ≥ 0 and therefore the graph of f touches the x axis at x = 0 and is above the x axis for all other values of xIf you don't include an equals sign, it will assume you mean "=0" It has not been well tested, so have fun with it, but don't trust it Clickanddrag to move the graph around If you just clickandrelease (without dragging), then the spot you clicked on will be the new center
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