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

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)

38+105= 143, 39+104=143, and you will find then adding the numbers on opposite sides, moving inwards yields the answer 138 every time. because of this, you’re going to multiply 138 times the number of pairs, which is 34. therefore, 34*138= 4692(i’m sorry if it’s the wrong numbers, but it’s the right concept)