Answer:
y = (x + 9)² + 9
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 a parabola in standard form : ax² + bx + c : a ≠ 0
the the x-coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
y = x² + 18x + 90 is in standard form
with a = 1, b= 18 and c = 90
[tex]x_{vertex}[/tex] = - [tex]\frac{18}{2}[/tex] = - 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
