Let's assume the equation is F(x) = x

To determine the intercepts at F(x) = 0, simply set the equation equal to zero and solve.

x

(x + 2)(x - 1) = 0

Roots are x = -2, x = 1.

To find the vertex, take the derivative and set it equal to zero, solve for the x and F(x) values.

F'(x) = 2x + 1

2x + 1 = 0

x = -1/2

F(-1/2) = (-1/2)

. = 1/4 - 1/2 - 2

. = -5/4

The vertex is at (-1/2, -5/4)

^{2}+ x - 2. You had a minus sign in there.To determine the intercepts at F(x) = 0, simply set the equation equal to zero and solve.

x

^{2}+ x - 2 = (x + 2)(x - 1)(x + 2)(x - 1) = 0

Roots are x = -2, x = 1.

To find the vertex, take the derivative and set it equal to zero, solve for the x and F(x) values.

F'(x) = 2x + 1

2x + 1 = 0

x = -1/2

F(-1/2) = (-1/2)

^{2}+ -1/2 - 2. = 1/4 - 1/2 - 2

. = -5/4

The vertex is at (-1/2, -5/4)