Answer:
f(x) = 2x² -16x +30
Step-by-step explanation:
You want the standard form quadratic function that has its vertex at (4, -2) and goes through the point (5, 0).
Vertex form
The vertex form of the quadratic with vertex (h, k) and vertical scale factor 'a' is ...
y = a(x -h)² +k
Using the given values, we can find 'a':
0 = a(5 -4)² -2
2 = a . . . . . . . . . add 2 and simplify
The vertex form of the function is ...
f(x) = 2(x -4)² -2
Expanding this, we have ...
f(x) = 2(x² -8x +16) -2
f(x) = 2x² -16x +30
