What is the leftmost x-intercept and the rightmost of 2x^2-3x-14?

Question

I am being asked to find the leftmost x-intercept and the rightmost x-interecept of 2x^2-3x-14. I am not sure how to do this. Can anyone help me?

Answer 1

Given 2x^2-3x-14

Parabola equation y = ax^2+bx+c

y = 2x^2-3x-14

To find x intercepts of parabola substiute y = 0 in above equation.

2x^2-3x-14 = 0

2x^2-7x+4x-14 = 0

x(2x-7)+2(2x-7) = 0

(2x-7)(x+2) = 0

2x-7 = 0 and x+2 = 0

Add 7 to each side

2x = 7

Divide to each side by 2.

x = 7/2

And x+2 = 0

Subtract 2 from each side.

x = -2

Left most x-intercept is -2.

Right most x-intercept is 7/2.