Find a function whose graph is a parabola with vertex (7, 8) and that passes through the point. (6, −9).

Work backwards from vertex form. Vertex form of a quadratic equation/parabola is the following: 

f(x) = a(x - h)² + k, where (h, k) is the vertex. 

f(x) = a(x - 6)² - 9 

Now, plug in the point that you're given to SOLVE FOR A. Remember that f(x) is just another way of writing y. 

8 = a(1)² - 9 
8 = a - 9 
a = 17 

So, plug in a = 17 into the equation. 

f(x) = 17(x - 6)² - 9 ←← your answer.

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