Question

Somebody please help so I can pass, please

Answer 1

First, we are going to find the vertex of our quadratic. Remember that to find the vertex $(h,k)$ of a quadratic equation of the form $y=a x^{2} +bx+c$, we use the vertex formula $h= \frac{-b}{2a}$, and then, we evaluate our equation at $h$ to find $k$.

We now from our quadratic that $a=2$ and $b=-32$, so lets use our formula:
$h= \frac{-b}{2a}$
$h= \frac{-(-32)}{2(2)}$
$h= \frac{32}{4}$
$h=8$
Now we can evaluate our quadratic at 8 to find $k$:
$k=2(8)^2-32(8)+56$
$k=2(64)-256+56$
$k=128-200$
$k=-72$
So the vertex of our function is (8,-72)

Next, we are going to use the vertex to rewrite our quadratic equation:
$y=a(x-h)^2+k$
$y=2(x-8)^2+(-72)$
$y=2(x-8)^2-72$
The x-coordinate of the minimum will be the x-coordinate of the vertex; in other words: 8.

We can conclude that:
The rewritten equation is $y=2(x-8)^2-72$
The x-coordinate of the minimum is 8

Answer 2

Answer:

y = 2 (x - 8 )2 + (-72)) .

The x-coordinate of the minimum is 8.

Step-by-step explanation:

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