Question

What is y=x^2-6x+7 in vertex form

Answer 1

(x - 3)² - 2

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 a parabola in standard form : ax² + bx + c : a ≠ 0

Then the x- coordinate of the vertex is

`x_(vertex)` = -
`(b)/(2a)`

y = x² - 6x + 7 is in standard form

with a = 1, b = - 6, c = 7, hence

`x_(vertex)` = -
`(-6)/(2)` = 3

substitute x = 3 into the equation for corresponding value of

y = 3² - 6(3) + 7 = 9 - 18 + 7 = - 2

(h, k) = (3, - 2), hence

y = (x - 3)² - 2 ← in vertex form

Answer 2

y = x^2 - 6x + 7

y = x^2 - 6x + 9 - 2

y = (x - 3)^2 - 2