Question

one x intercept for a parabola is at the point (1,0). use the factor method to find the other x intercept for the parabola defined by y=-5x^2+15x-10

Answer 1

First simplify the equation of parabola y=-5x^2+15x-10 in the following way:

D=(15)^2-4\cdot (-5) \cdot (-10)=225-200=25, \\ \sqrt{D}=5, \\ x_{1,2} = \dfrac{-15\pm 5}{2\cdot(-5)} = 2, 1 \\ -5x^2+15x-10=-5(x-1)(x-2), \\ y=-5(x-1)(x-2).

You can see that if x=1 or x=2, then y=0. Two points of intersection with x-axis are (1,0) and (2,0).