[URGENT]
A family of parabolas have rules of the form y = ax^{2} + c. For the parabola in this family that passes through the point (-1, 4) and (0, 8), find the values of a and c.

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y = ax² + c thru (-1,4) and (0,8)

Substituting in the coordinates of each point for x and y gives two equations:

4 = a  (-1)² + c

8 = a (0²) + c = c

From the second one we see c=8.  Substituting into the first one,

4= a + 8

a = 4-8 = -4

a=-4, c=8

Check:

f(x) = -4x² + 8

f(0) = 8, good

f(-1) = -4(1) + 8 = 4, good

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step-by-step explanation: