Explanation Given: The quadratic equation is f ( x ) = − 2 x 2 + 3 x − 2 . Formula used: For graphing the quadratic equation, f ( x ) = a x 2 + b x + c , a ≠ 0 : 1) The coordinates of the vertex are ( − b 2 a , f ( − b 2 a ) ) . 2) The y -intercept is at f ( 0 ) . 3) The x -intercepts (if they exist) occur where f ( x ) = 0 . And, The quadratic formula: a x 2 + b x + c = 0 x = − b ± b 2 − 4 a c 2 a Calculation: Consider the provided quadratic equation, f ( x ) = − 2 x 2 + 3 x − 2 Since a = − 2 , b = 3 , and c = − 2 . So, the vertex occurs at x = − b 2 a . Then, x = − 3 2 ( − 2 ) = 3 4 To find the y -coordinate, calculate f ( 3 4 )

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ISBN: 9780135910023

Author: Tobey, John, Slater, Jeffrey, Blair, Jamie , Crawford, Jenny

Publisher: PEARSON

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Chapter 8.5, Problem 8E

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To calculate: The coordinates of the vertex, the y-intercept, and the x-intercepts of the quadratic equation, f(x)=−2x2+3x−2.

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Chapter 8.5, Problem 7E

Chapter 8.5, Problem 9E

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1. Given that h(t) = -5t + 3 t². A tangent line H to the function h(t) passes through the point (-7, B). a. Determine the value of ẞ. b. Derive an expression to represent the gradient of the tangent line H that is passing through the point (-7. B). c. Hence, derive the straight-line equation of the tangent line H 2. The function p(q) has factors of (q − 3) (2q + 5) (q) for the interval -3≤ q≤ 4. a. Derive an expression for the function p(q). b. Determine the stationary point(s) of the function p(q) c. Classify the stationary point(s) from part b. above. d. Identify the local maximum of the function p(q). e. Identify the global minimum for the function p(q). 3. Given that m(q) = -3e-24-169 +9 (-39-7)(-In (30-755 a. State all the possible rules that should be used to differentiate the function m(q). Next to the rule that has been stated, write the expression(s) of the function m(q) for which that rule will be applied. b. Determine the derivative of m(q)

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Chapter 8 Solutions

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The coordinates of the vertex, the y -intercept, and the x -intercepts of the quadratic equation , f ( x ) = − 2 x 2 + 3 x − 2 .

Solution Summary: The author calculates the coordinates of the vertex, y -intercept, and x intercepts in the quadratic equation.

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To calculate: The coordinates of the vertex, the y-intercept, and the x-intercepts of the quadratic equation, f(x)=−2x2+3x−2.

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Chapter 8 Solutions