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

Answer 1

The given quadratic function is in the form of y = ax^2+bx+c.

In this case, a = -1, b = 8, and c = -12.

The x-coordinate of the vertex can be found using the formula x = -b/(2a).
So, x = -8/(2*(-1)) = 4.

To find the y-coordinate of the vertex, substitute x = 4 back into the original equation:
y = -(4)^2 + 8(4) - 12 = 8.

Therefore, the vertex is (4, 8).

The axis of symmetry is a vertical line that passes through the vertex. The equation for the axis of symmetry is x = h, where h is the x-coordinate of the vertex.
So, the axis of symmetry is x = 4.