Question

Determine the vertex and axis of symmetry of y=−x2+8x+7

Answer 1

To determine the vertex and axis of symmetry of the quadratic equation y = -x^2 + 8x + 7, we observe the general form of a quadratic equation: y = ax^2 + bx + c.

Comparing this to our equation, we have a = -1, b = 8, and c = 7.

To find the x-coordinate of the vertex, we use the formula x = -b/2a:

x = -(8)/(2(-1))
x = -8/(-2)
x = 4

Substituting x = 4 back into the equation y = -x^2 + 8x + 7 to find the y-coordinate of the vertex:

y = -(4)^2 + 8(4) + 7
y = -16 + 32 + 7
y = 23

Therefore, the vertex is (4, 23).

To find the axis of symmetry, we simply take the x-coordinate of the vertex:

Axis of symmetry: x = 4