Question

How do you write y=4x^2 -64x -265 in vertex form

Answer 1

y = (x - 8)² - 521

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

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

y = 4x² - 64x - 265 is in standard form

with a = 4, b= - 64 and c = - 265

`x_(vertex)` = -
`(-64)/(8)` = 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