Question

Determine the vertex and axis of symmetry of y=-x^2+8x-12

The vertex is :
The axis of symmertry is :

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine the vertex and axis of symmetry of the quadratic equation y = -x^2 + 8x - 12, we can first rewrite the equation in vertex form.

The vertex form of a quadratic equation is given by y = a(x - h)^2 + k, where (h, k) is the vertex.

Let's complete the square to rewrite the equation in vertex form:

y = -x^2 + 8x - 12
= -(x^2 - 8x) - 12

To complete the square, we take half the coefficient of x (-8/2 = -4) and square it to get 16. We add and subtract 16 inside the parentheses:

y = -(x^2 - 8x + 16 - 16) - 12
= -(x^2 - 8x + 16) + 16 - 12
= -(x - 4)^2 + 4

Now the equation is in vertex form y = a(x - h)^2 + k, where h = 4 and k = 4. Therefore, the vertex is (4, 4).

The axis of symmetry is the vertical line that passes through the vertex. In this case, the axis of symmetry is x = 4.