Question

Which of the following options represents the quadratic function y = ax^2 + bx + c that is equivalent to the vertex form y = 2(x – 4)^2 + 5?

A) y = 2x^2 - 16x + 37
B) y = 2x^2 - 8x + 21
C) y = 2x^2 - 8x + 5
D) y = 2x^2 - 16x + 21

Answer 1

The vertex form y = 2(x – 4)^2 + 5, when expanded, yields the standard form y = 2x^2 - 16x + 37, which is option A.

Step-by-step explanation:

The quadratic function in vertex form, y = 2(x – 4)^2 + 5, can be expanded to standard form by squaring the binomial and distributing the leading coefficient. Here are the steps to expand:

1. First, square the binomial: (x - 4)^2 = x^2 - 8x + 16.
2. Multiply through by the coefficient 2: 2(x^2 - 8x + 16) = 2x^2 - 16x + 32.
3. Add the constant term +5: 2x^2 - 16x + 32 + 5 = 2x^2 - 16x + 37.

Therefore, the quadratic function y = 2x^2 - 16x + 37 is equivalent to the vertex form given.