Question

What is the equation for each parabola in y=a(x-r)(x-s) form?Please explain it step by step

Answer 1

1. first parabola is up, so a are going to be positive
y = a(x-r)(x-s), 
roots -7,-3, so we can write y=a(x+7)(x+3)   [1]
we can take point (-5,-2), substitute into equation [1], and find value of a
-2=a(-5+7)(-5+3)
-2=a*2*(-2)
a=1/2
so first parabola has an equation 
y=1/2(x+7)(x+3) 

2. second parabola
y=a(x-r)(x-s)      roots are 2 and 4 so we ca write
y=a(x-2)(x-4) take point (3,4) and substitute into this equation
4 =a(3-2)(3-4)
4=-a
a=-4, and it will look down
y=-4(x-2)(x-4)