Question

which equation and ordered pair represent the correct vertex form and vertex for j(x) = x^2 - 12 x +7?

Answer 1

see explanation

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 the equation in standard form : ax² + bx + c : a ≠ 0

then the x-coordinate of the vertex is

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

j(x) = x² - 12x + 7 is in standard form

with a = 1, b = - 12 and c = 7, hence

`x_(vertex)` = -
`(-12)/(2)` = 6

substitute x = 6 into j(x) for y- coordinate

y = 6² - 12(6) + 7 = 36 - 72 + 7 = - 29

vertex = (6, - 29 ) and

j(x) = (x - 6)² - 29 ← equation in vertex form