Determine the vertex and axis of symmetry of y=−x2+8x+7
(2 points)
To determine the vertex and axis of symmetry of the quadratic equation y = -x^2 + 8x + 7, we need to convert it into vertex form, which is in the form of y = a(x - h)^2 + k.
To do this, we will complete the square:
y = -x^2 + 8x + 7
= -(x^2 - 8x) + 7
= -(x^2 - 8x + 16) + 7 + 16 (adding and subtracting (-8/2)^2)
= -(x - 4)^2 + 23
Comparing this with the vertex form, we can determine that the vertex of the equation is (h, k) = (4, 23).
The axis of symmetry is the vertical line passing through the vertex. Since the x-coordinate of the vertex is 4, the equation of the axis of symmetry is x = 4.