Write the equations of the parabolas with the following conditions:?

Question

Write the equations of the parabolas with the following conditions:

a) with vertex (5,-3) and passing through (3,9)

b) passing through the points (-1,-6), (3,-12), and (2,-4.5)

Answer 1

If (5, -3) is the vertex, find the "matching" point for (3,9) which is (7,9)

The write 3 equations plugging in the x and y values into the general equation

y = ax^2 + bx + c

-3 = a(5^2) + b(5) + c

9 = a(3^2) + b(3) + c

9 = a(7^2) + b(7) + c

and solve simultaneously

Do that for b as well