Explanation Given information: The provided function is: f ( x ) = − x 2 − 40 x + 500 Graph: Consider the function, f ( x ) = − x 2 − 40 x + 500 Compare the equation f ( x ) = − x 2 − 40 x + 500 with the standard function f ( x ) = a x 2 + b x + c and find the value of a , b and c . The values are a = − 1 , b = − 40 and c = 500 . since a < 0 , therefore the parabola will be downward facing, To graph a quadratic function, four things should be calculated first. (i) Vertex (ii) x -intercept (iii) y - intercept (iv) symmetry Vertex: The formula of x- coordinate of vertex is, x = − b 2 a Substitute a = − 1 and b = − 40 in the equation x = − b 2 a . x = − ( − 40 ) 2 ( − 1 ) = − 20 The y- coordinate of vertex, Substitute x = − 20 in the function f ( x ) = − x 2 − 40 x + 500 . f ( x ) = − ( − 20 ) 2 − 40 ( − 20 ) + 500 = − 400 + 800 + 500 = 900 Thus, coordinates of the vertex are ( − 20 , 900 ) . x -intercept: To calculate x -intercept of the function, substitute f ( x ) = 0 in the equation f ( x ) = − x 2 − 40 x + 500 and solve. − x 2 − 40 x + 500 = 0 − x 2 − 50 x + 10 x + 500 = 0 − x ( x + 50 ) + 10 ( x + 50 ) = 0 ( − x + 10 ) ( x + 50 ) = 0 Now solve for − x + 10

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ISBN: 9781337291248

Author: Waner, Stefan.

Publisher: Cengage Learning,

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Chapter 2.1, Problem 11E

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To graph: The function f(x)=−x2−40x+500 and indicate the coordinates of the vertex, the y-intercept and x-intercept.

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Chapter 2.1, Problem 10E

Chapter 2.1, Problem 12E

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To graph: The function f ( x ) = − x 2 − 40 x + 500 and indicate the coordinates of the vertex, the y -intercept and x -intercept.

Solution Summary: The author compares the function f(x)=-x 2-40x+500 with the standard function and finds the values of a,b, and c.

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To graph: The function f(x)=−x2−40x+500 and indicate the coordinates of the vertex, the y-intercept and x-intercept.

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