Question

what is the vertex form of the following equation?

y = -x^2 + 2x - 10

Answer 1

[AI-generated answer — Bot GPT 3.5]

To transform the given equation into vertex form, we need to complete the square. The vertex form of a quadratic equation is y = a(x - h)^2 + k, where (h, k) represents the coordinates of the vertex.

Given equation: y = -x^2 + 2x - 10

To complete the square, we need to take the coefficient of x, which is 2, divide it by 2, and then square the result: (2/2)^2 = 1

Add this value inside the parentheses (x - h) and subtract it outside to maintain the balance.

y = -x^2 + 2x - 10
= -(x^2 - 2x + 1) - 10 + 1 (adding and subtracting 1 inside the parentheses)
= -(x^2 - 2x + 1) - 9

Now, we can rewrite the equation in the vertex form:

y = -(x - 1)^2 - 9

Thus, the vertex form of the equation y = -x^2 + 2x - 10 is y = -(x - 1)^2 - 9.