9 Find the equation of a parabola with the following conditi

9). Find the equation of a parabola with the following conditions.

a). Vertex (0,-3), passing through (2,4)

b). Vertex (4,-7), with x-intercept (3)

gen equation of parabola:

y = a(x -h)^2 +k

where (h,k) is vertex :

y = a(x-0)^2 -3 -----> y = ax^2 -3

now find value of a from point (2,4)

4 = a(2^2) -3 ----> 4 = 4a -3

4a = 7 ---> a = 7/4

y = (7/4)x^2 -3

b) Vertex (4,-7), with x-intercept (3)

y = a(x-h)^2 +k

y =a( x-4)^2 -7

now find a from the point (3, 0)

0 = a(3-4)^2 -7

0 = a-7

a =7

y = 7(x -4)^2 -7