Answer:
y = (x - 8)² - 521
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 quadratic in standard form : ax² + bx + c : a ≠ 0
then the x-coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
y = 4x² - 64x - 265 is in standard form
with a = 4, b= - 64 and c = - 265
[tex]x_{vertex}[/tex] = -[tex]\frac{-64}{8}[/tex] = 8
substitute x = 8 into the equation for y-coordinate
y = 4(8)² - 64(8) - 265 = 256 - 512 - 265 = - 521
y = (x - 8)² - 521 ← in vertex form
