Let's assume the equation is F(x) = x2 + 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.
x2 + 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)
To determine the intercepts at F(x) = 0, simply set the equation equal to zero and solve.
x2 + 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)
