Book edition Middle English Edition

Author(s) Carter

Pages 804 pages

ISBN 9780079039903

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Short Answer

Find the coordinates of the maximum or minimum value of each quadratic equation to the nearest hundredth.

$f (x) = - 6 x^{2} + 9 x$

The coordinates of the minimum value of the quadratic equation $f (x) = - 6 x^{2} + 9 x$ to the nearest hundredth is $(0.75, 3.375)$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information.

Given to determine the coordinates of the maximum or minimum value of the quadratic equation $f (x) = - 6 x^{2} + 9 x$ to the nearest hundredth.

Step 2. Explanation.

The maximum or minimum value of a quadratic function lies at the vertex of the graph.

For an equation of the form $f (x) = a x^{2} + b x + c$ :

If $a > 0$ , it is an upwards opening parabola and so has a minimum value

If $a < 0$ , it is a downwards opening parabola and so has a maximum value.

So, the given quadratic equation has a maximum value.

For an equation of the form $f (x) = a x^{2} + b x + c$ , the x-coordinate of the vertex is given by $x = - \frac{b}{2 a}$

Here for the given equation, $a = - 6, b = 9$

Plugging the values in the equation:

$\begin{array}{l} x = - \frac{b}{2 a} \\ x = - \frac{(9)}{2 (- 6)} \\ x = \frac{9}{12} \\ x = 0.75 \end{array}$

Hence the x-coordinate of the vertex is $x = 0.75 .$

So, the y-coordinate of the vertex can be obtained by plugging the value in the equation.

Plugging $x = 0.75$ in the equation:

$\begin{array}{l} f (x) = - 6 x^{2} + 9 x \\ f (0.75) = - 6 {(0.75)}^{2} + 9 (0.75) \\ f (0.75) = - 3.375 + 6.75 \\ f (0.75) = 3.375 \end{array}$

Hence the coordinates of the vertex is $(0.75, 3.375)$ .

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Algebra 2

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Short Answer

Find the coordinates of the maximum or minimum value of each quadratic equation to the nearest hundredth.

$f (x) = - 6 x^{2} + 9 x$

Step by Step Solution

Step 1. Given Information.

Step 2. Explanation.

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Algebra 2

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Short Answer

Find the coordinates of the maximum or minimum value of each quadratic equation to the nearest hundredth. fx=-6x2+9x

Step by Step Solution

Step 1. Given Information.

Step 2. Explanation.

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Find the coordinates of the maximum or minimum value of each quadratic equation to the nearest hundredth.

$f (x) = - 6 x^{2} + 9 x$