Finding the value of $x$ $x$ given $y$ $y$ is a maximum? See picture below

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Finding the value of $x$ $x$ given $y$ $y$ is a maximum? See picture below

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Answer 1 · 2017-04-09T17:50:21

When given an equation of the form $y = a x^{2} + b x + c$ $y = ax^2+bx+c$ , where "a" is negative, the maximum value is the y coordinate of the vertex. The x coordinate of the vertex is:
$h = - \frac{b}{2 a}$ $h=-b/(2a)$

Explanation:

Given: $y = - 16 x^{2} + 160 x - 256$ $y = -16x^2 + 160x - 256$

We observe that $a = - 16$ $a = -16$ and $b = 160$ $b = 160$

The x coordinate of the vertex is:

$h = - \frac{b}{2 a}$ $h = -b/(2a)$

$h = - \frac{160}{2 (- 16)}$ $h = -160/(2(-16))$

$h = 5 \leftarrow$ $h = 5 larr$ this is the answer to [7.a.i]

The maximum value is the function evaluated at $x = h = 5$ $x = h = 5$ :

$y = - 16 {(5)}^{2} + 160 (5) - 256$ $y = -16(5)^2+160(5)-256$

$y = 144 \leftarrow$ $y = 144 larr$ this is the answer to [7.a.ii]

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