Explanation Given information: The provided function: f ( x ) = x 2 + x − 1 Graph: Consider the function, f ( x ) = x 2 + x − 1 Compare the equation f ( x ) = x 2 + x − 1 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 = − 1 . Since, a > 0 therefore the parabola will be upward 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 ) = − 0.5 The y- coordinate of vertex, Substitute x = − 0.5 in the function f ( x ) = x 2 + x − 1 . f ( x ) = ( − 0.5 ) 2 + ( − 0.5 ) − 1 = 0.25 − 0.5 − 1 = − 0.25 − 1 = − 1.25 Thus, coordinates of the vertex are ( − 0.5 , − 1.25 ) . x -intercept: To calculate x -intercept of the function, substitute f ( x ) = 0 in the equation f ( x ) = x 2 + x − 1 and solve. x 2 + x − 1 = 0 To find the value of x use the formula, x = − b ± b 2 − 4 a c 2 a Substitute a = 1 , b = 1 and c = − 1 in the equation x = − b ± b 2 − 4 a c 2 a

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ISBN: 9781337291248

Author: Waner, Stefan.

Publisher: Cengage Learning,

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Chapter 2.1, Problem 13E

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To graph: The function f(x)=x2+x−1 and indicate the coordinates of the vertex, the y-intercept and x-intercept.

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Chapter 2.1, Problem 12E

Chapter 2.1, Problem 14E

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To graph: The function f ( x ) = x 2 + x − 1 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-1 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−1 and indicate the coordinates of the vertex, the y-intercept and x-intercept.

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Chapter 2 Solutions