Explanation Given information: The provided function is: f ( x ) = − x 2 − x Graph: Consider the function, f ( x ) = − x 2 − x Compare the equation f ( x ) = − x 2 − x 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 = − 1 and c = 0 . 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 = − 1 in the equation x = − b 2 a . x = − ( − 1 ) 2 ( − 1 ) = − 1 2 = − 0.5 The y- coordinate of vertex, Substitute x = − 0.5 in the function f ( x ) = − x 2 − x . f ( x ) = − ( − 0.5 ) 2 − ( − 0.5 ) = − 0.25 + 0.5 = 0.25 Thus, coordinates of the vertex are ( − 0.5 , 0.25 ) . x -intercept: To calculate x -intercept of the function, substitute f ( x ) = 0 in the equation f ( x ) = − x 2 − x and solve

7th Edition

ISBN: 9781337514309

Author: Waner

Publisher: Cengage

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Chapter 2.1, Problem 8E

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

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Chapter 2.1, Problem 7E

Chapter 2.1, Problem 9E

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

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

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

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