What is the vertex of the following function? f(x) = 2(x+8)^2 - 2

1 answer:

4 0

$~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ f(x)=2(x+8)^2-2\implies f(x)=2[x-(\stackrel{h}{-8})]^2\stackrel{k}{-2}~\hfill \stackrel{vertex}{(-8~~,~~-2)}$

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Micah places a mirror on the ground 24 feet from the base of a tree. He walks

irina [24]

The height of tree is 8 feet

<h3><u>Solution:</u></h3>

Given, Micah places a mirror on the ground 24 feet from the base of a tree

At that point, Micah's eyes are 6 feet above the ground

And he is 9 feet from the image in the mirror.

To find : height of tree = ?

Let "n" be the height of tree

From the question, we can see there is a directly proportional relationship between heights and distances.

Proportional relationships are relationships between two variables where their ratios are equivalent.

$\frac{\text { height of micah eyes above ground }}{\text { distance of micah from mirror }}=\frac{\text { height of tree above the ground }}{\text { distance of tree from mirror }}$

$\begin{array}{l}{\frac{6 \text { feet }}{9 \text { feet }}=\frac{n \text { feet }}{24 \text { feet }}} \\\\ {\frac{6}{9}=\frac{n}{24}} \\\\ {\text { n }=\frac{1}{3} \times 24} \\\\ {\text { n }=8}\end{array}$