Question

Write y=2x^2-12x+16 in vertex form.

Answer 1

To write the quadratic equation y = 2x^2 - 12x + 16 in vertex form, we can complete the square to find the vertex. The vertex form is y = 2(x - 3)^2 + 16.

Step-by-step explanation:

To write the quadratic equation y = 2x^2 - 12x + 16 in vertex form, we can complete the square. This form can be written as y = a(x - h)^2 + k, where (h, k) is the vertex. To complete the square, we need to find the values of h and k:

1. Let's rearrange the equation by factoring out the coefficient of x^2: y = 2(x^2 - 6x) + 16.
2. Now, we take half of the coefficient of x (-6), square it, and add it inside the parenthesis: y = 2(x^2 - 6x + (-6/2)^2) + 16.
3. Simplifying inside the parenthesis, we get: y = 2(x^2 - 6x + 9) + 16.
4. The vertex form is now obtained as: y = 2(x - 3)^2 + 16.

Therefore, the quadratic equation y = 2x^2 - 12x + 16 can be written in vertex form as y = 2(x - 3)^2 + 16.