Question

If f(x) is a parabola with vertex (2,−1) whose equation isf(x) =ax2+bx+c, what are the values of a, b, c if the graph off intersects the y-axis at the point (0,3).

Answer 1

(a, b, c) = (1, -4, 3)

Explanation:

In vertex form, the equation is ...

... f(x) = a(x -2)² -1

This has a y-intercept of ...

... f(0) = a(0 -2)² -1 = 4a -1

We want that value to be 3, so we can find "a" as ...

... 4a -1 = 3 . . . . . set f(0) = 3

... 4a = 4 . . . . . . . add 1

... a = 1 . . . . . . . . divide by 4

Then ...

... f(x) = (x -2)² -1 = x² -4x +3

The coefficients are a=1, b=-4, c=3.