Complete the square to determine the vertex and axis of symmetry of y=−x^2+8x+7

Answer 1

To complete the square in the quadratic equation y = -x^2 + 8x + 7, we need to focus on the terms involving x.

First, let's rearrange the equation:

y = -(x^2 - 8x) + 7

Next, we want to take half of the coefficient of x, square it, and add it to both sides:

y = -(x^2 - 8x + 16) + 7 + 16
= -(x^2 - 8x + 16) + 23

Now, we can rewrite the expression inside the parentheses as a perfect square:

y = -(x^2 - 8x + 16) + 23
= -(x - 4)^2 + 23

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

From our equation, we can see that the vertex is (4, 23), and the axis of symmetry is x = 4.