Answer: y = (-4/9)x2 + (16/9)x + (47/9)
Step-by-step explanation:
f(x) = a(x - h)2 + k, where the vertex is (h,k) = (2,7) while passing through the point (x,y) = (-1,3). We must plug everything in to solve for a first. Then,
3 = a(-1 - 2)2 + 7
3 = a(-3)2 + 7................Subtract 7 to both sides such that
-4 = 9a...............Then divide 9 such that
a = (-4/9)
Now we plug a into the equation with the vertex to create the parabolic function such that
y = (-4/9)(x - 2)2 + 7 ..............Then FOIL the (x-2)2 such that
y = (-4/9)(x2 - 4x + 4) + 7..............Then distribute the (-4/9) inside such that
y = (-4/9)x2 + (16/9)x - (16/9) + 7.............Then (-16/9) + 7 = (-16/9) + (63/9) = 47/9
so, y = (-4/9)x2 + (16/9)x + (47/9)
