Question

Write Y=x^2+18x+90 In vertex form

Answer 1

y = (x + 9)² + 9

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

the the x-coordinate of the vertex is

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

y = x² + 18x + 90 is in standard form

with a = 1, b= 18 and c = 90

`x_(vertex)` = -
`(18)/(2)` = - 9

to find the corresponding y-coordinate substitute x = - 9 into the equation

y = (- 9)² + 18(- 9) + 90 = 81 - 162 + 90 = 9

⇒ y = (x + 9)² + 9 ← in vertex form