Question

Type the correct answer In each box. Use numerals Instead of words. If necessary, use / for the fraction bar(s). Rewrite the following equation in the form Y=(a(x-h)^2+k Then, determine the x-coordinate of the minimum.$y2 {x}^{2} \times 32 x + 56$The rewritten equation is Y= _____(x-____)^2 +____The x-coordinate of the minimum Is ____//

Answer 1

We are given the following quadratic equation

$y=2x^2-32x+56$

We are asked to convert this equation into the vertex form given by

$y=a(x-h)^2+k_{}$

Let us convert the given quadratic equation into the above form.

$\begin{gathered} y=2x^2-32x+56 \\ y-56=2x^2-32x \\ y-56=2(x^2-16x) \end{gathered}$

Now we have to add a number to both sides of the equation such that the terms inside the parenthesis become perfect squares.

How about 64?

$y-56+128=2(x^2-16x+64)$

Why did we add 128 on the left side?

Because 64 is being multiplied by 2 on the right side of the equation so 64x2 = 128

$\begin{gathered} y-56+128=2(x^2-16x+64) \\ y+72=2(x-8)^2 \\ y=2(x-8)^2-72 \end{gathered}$

As you can see, the equation has been converted into the vertex form.

Finally, the x-coordinate of the minimum is

The value of h is the x-coordinate of the minimum and the value of k is the y-coordinate of the minimum

Comparing the above equation with the standard vertex form, we see that

h = 8

Therefore, 8 is x-coordinate of the minimum