Question

The equation y=3x2 - 24x+ 45 is in standard form. Write the equation in vertex form.

A. y=3(x-4)2 - 3
B. y=3(x-24)2 + 45
C. y=3(x-8)2 + 15
D. y=(x– 8)2 + 15

Answer 1

A. y = 3(x -4)^2 -3

Explanation:

y = 3x^2 - 24x + 45

Use the form ax^2 + bx + c

whereas a = 3, b = -24, c =45

Consider the vertex form of a parabola

a(x + d)^2 + e

Since d = b/2a = -24/2(3) = -4

And e = c - (b)^2/4a = 45 - (-24)^2/4(3) = 45 - 48 = -3

So y = a(x + d)^2 + e

y = 3(x -4)^2 -3