What I the quadratic formula for (0,0) , (1,-4) , (5,0)

Question

X and Y axis

Answer 1

Let y=ax²+bx+c be the quadratic containing the given points. We have to find constants a, b and c.

When x=0, y=0 (the point (0,0)), so 0=c, i.e., c=0.

When x=1, y=-4 (the point (1,-4)), so -4=a+b. Therefore, b=-a-4=-(a+4).

When x=5, y=0 (the point (5,0), so x=5 is the x-intercept and 0=25a+5b.

Substitute for b: 0=25a-5(a+4)=25a-5a-20, 20a=20, a=1, so b=-(1+4)=-5.

y=x²-5x.