Question

Find a function whose graph is a parabola with vertex (4,-23) and that passes through the point (5,-21). Please show work.

Answer 1

vertex form
\[y = a(x-h)^{2} + k\]
vertex: (h,k)
h = 4
k = -23
\[y = a(x-4)^{2} - 23\]
Now use the point (5,-21) to solve for a
substitute 5 for x, -21 for y
\[-21 = a(5-4)^{2} -23\]
\[-21 = a - 23\]
\[a = 2\]
Then the function is
\[y = 2(x-4)^{2} - 23\]