Question

What is the vertex form of the equation y = 3(x-2)^2 - (x-5)^2?

A) y = 3(x-2)^2 - (x-5)^2
B) y = 3(x^2 - 4x + 4) - (x^2 - 10x + 25)
C) y = 3x^2 - 12x + 12 - x^2 + 10x - 25
D) y = 2x^2 - 2x + 3

Answer 1

The vertex form of the given equation is y = 2x^2 - 2x + 3.

Step-by-step explanation:

The vertex form of a quadratic equation is given by y = a(x-h)^2 + k, where (h,k) represents the vertex of the parabola. In the given equation y = 3(x-2)^2 - (x-5)^2, the vertex form can be obtained by expanding the equation:

y = 3(x^2 - 4x + 4) - (x^2 - 10x + 25)

Simplifying further, we get y = 3x^2 - 12x + 12 - x^2 + 10x - 25. Therefore, the vertex form of the equation is y = 2x^2 - 2x + 3 (option D).