solve. f(x)= x^-5x-6?

Let’s start with the easiest thing to find: the x- and y-intercepts.

The y-intercept is found by replacing x with 0.

f(0) = 0^2 – 5(0) – 6

f(0) = -6

The y-intercept is (0,-6)

The x-intercept is found by setting f(x) equal to zero.

0 = x^2 – 5x – 6

This can be solved by factoring.

0 = (x-6)(x+1)

x-6 = 0 or x+1 = 0

x = 6 or x = -1

The x-intercepts are (6,0) and (-1,0)

You can find the vertex by completing the square.

f(x) = x^2 – 5x + 6

f(x) = (x^2 – 5x + (5/2)^2) – 6 – 25/4

f(x) = (x – 5/2)^2 – 49/4

The vertex is (5/2, 49/4)

The axis of symmetry is just the x coordinate of the vertex.

x = 5/2