Question

What are the x-intercepts of the graph of the quadratic functionf(x)=x2-x-6?A) (3,0) and (2,0)B) (-3,0) and (-2,0)C) (3,0) and (-2,0)D) (-3,0) and (2,0)

Answer 1

The given equation of quadratic :

`f(x)=x^2-x-6`

for the x - intercept :

The y coordinates are equal to 0

Substitute f(x) = 0

`\begin{gathered} f(x)=x^2-x-6 \\ x^2-x-6=0 \end{gathered}`

Simplify the expression for x :

`\begin{gathered} x^2-x-6=0 \\ x^2-3x+2x-6=0 \\ x(x-3)+2(x-3)=0 \\ (x+2)(x-3)=0 \end{gathered}`

Thus : x + 2= 0 and x - 3 = 0

so, x = -2 and x = 3

X intercept are ( -2, 0) & ( 3, 0)