What is the equation of the parabola with vertex ( 3, -20) and that passes through point ( 7, 12)

Step-by-step explanation:

y = a(x - h)² + k    - vertex form of  the equation of the parabola with vertex (h, k)

So  the equation of the parabola with vertex (3, -20):

y = a(x - 3)² + (-20)

y = a(x - 3)² - 20

The parabola passes through point (7, 12) so if x=7 then y=12

12 = a(7 - 3)² + (-20)

12 +20 = a(4)² - 20 +20

32 = 16a

a = 2

Therefore the equation of the parabola with vertex (3, -20) and that passes through point (7, 12):

                   y = 2(x - 3)² - 20

d perpendicular bisected and midpoint