Which equation is y = 2x2 – 8x + 9 rewritten in vertex form?

y = 2(x - 2)² + 1

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Given

y = 2x² - 8x + 9

Using the method of completing the square

Factor out 2 from the first 2 terms

y = 2(x² - 4x) + 9

add/subtract ( half the coefficient of the x- term )² to x² - 4x

y = 2(x² + 2(- 2)x + 4 - 4) + 9

   = 2(x - 2)² - 8 + 9

   = 2(x - 2)² + 1 ← in vertex form

a.

step-by-step explanation:

step 1 distribute 2 to every term in the parentheses

step 2 add 10 on both sides of the equal sign

3. (5x + 1) - (-10x + 6)

simplify the answer choice. combine like terms. remember to distribute the negative to the terms inside the second parenthesis. also remember that two negatives = one positive, and one of each sign = negative.

- (-10x + 6) = + 10x - 6

simplify. combine like terms:

5x + 1 + 10x - 6

5x + 10x + 1 - 6

15x - 5

∴ it is your answer

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