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. y = 2x2 - 32x + 56

Answer 1

• Vertex Form: y = a(x - h)^2 + k, with (h,k) as the vertex.

To convert it into vertex form, we are going to be completing the square. Firstly, subtract 56 on both sides: $y-56=2x^2-32x$

Next, factor out the GCF, or greatest common factor, of the right side. To find the GCF, list the factors of both terms and the greatest one they share is their GCF. In this case, the GCF is 2: $y-56=2(x^2-16x)$

Next, we want to make what's inside the parentheses a perfect square. To find the constant of the perfect square, divide the x term by 2 and square the quotient. In this case:

-16 ÷ 2 = -8, (-8)² = 64

So you're gonna have to add 64 to the inside of the parentheses. To cancel this out, you will need to add to the other side the product of 64 and 2 (since 64 is inside the parentheses), which is 128: $y+72=2(x^2-16x+64)$

Next, factor the polynomial inside the parentheses: $y+72=2(x-8)^2$

Next, subtract 72 on both sides and your vertex form is $y=2(x-8)^2-72$

Now looking at this vertex form, the vertex is (8,-72), which means that the x-coordinate of the vertex is 8.