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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

The rewritten equation is y =
(x -
)2 +
.

The x-coordinate of the minimum is
.

Type the correct answer in each box Use numerals instead of words If necessary use for the fraction bars Rewrite the following equation in the form y ax h2 k Th class=

Respuesta :

ponton

Answer:

a=2

h=8

k=-72

Step-by-step explanation:

[tex]y = 2 {x}^{2} - 32x + 56 \\ = 2( {x}^{2} - 16x + 28) \\ = 2( {x}^{2} - 2 \times 8 x + 64 - 36) \\ = 2 {(x - 8)}^{2} - 72 \\ then \: the \: minimum \: is \: - 72 \: and \\ \: the \: x - coordinate \: of \: minimum \: is \: 8.[/tex]

The rewritten equation is 2(x-8)^2 - 100, and the x-coordinate of the minimum is 8.

What is a quadratic equation?

A quadratic equation is a second-degree algebraic equation in x. The conventional form of the quadratic equation is ax^2 + bx + c = 0, with a and b as coefficients, x as the variable, and c as the constant component.

y = 2x^2 - 32x + 56

y = 2(x^2 - 16x + 28)

y = 2((x^2 - 16x + 64) - 36)

y = 2((x - 8)^2 - 36)

y = 2(x - 8)^2 - 72

The equation when converted in the form  y = a(x - h)^2 + k will look like  y = 2(x - 8)^2 - 72.

The minimum value of this function is y = -72 and the x-coordinate of the minimum is x = 8.

Learn more about quadratic equations on:

https://brainly.com/question/1214333

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