Find the vertex and axis of symmetry of the function. f(x) = -x² + 14x + 9.

Solution:

Given function:

f(x) = -x² + 14x + 9.

The axis of symmetry is the x-coordinate of the vertex, a vertical line across which the graph exhibits symmetry, given by x = -b/2a when the quadratic is in the form ax² + bx + c

Here, we see b = 14,

a = -1; the axis is x = -14/2(-1) = 7

The coordinates of the vertex are given by (-b/2a, f(-b/2a))

We know -b/2a = 7, so we need to find f(7).

f(7) = -7² + 14(7) + 5 = -49 + 98 + 5 = 54

The vertex is then (7, 54)

Find the vertex and axis of symmetry of the function. f(x) = -x² + 14x + 9.

Summary:

The vertex and axis of symmetry of the function. f(x) = -x² + 14x + 9 is (7, 54) and x = 7.