Mark M. answered • 12/02/14

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Mathematics Teacher - NCLB Highly Qualified

Think that the highest point is on the vertical axis. Its coordinates are (0, 45).

The two points at which it touches the ground are (-30, 0) and (30, 0).

The zeros of the function are ±30.

f(x) = ax

^{2}+ bx + c45 = a(0)

^{2}+ 0b + c45 = c

0 = a(30)

^{2}+ 30b + 450 = 900a + 30b + 45

and

0 = a(30)

0 = 900a - 30b + 45

^{2}- 30b + 450 = 900a - 30b + 45

Using elimination by adding

0 = 1800a + 90

-90 = 1800a

-1/20 = a

Substituting into either of the two above

0 = -(30)

^{2}/20 + 30b + 450 = -900/20 + 30b + 45

0 = -45 + +30b + 45

0 = b

f(x) = -x

^{2}/20 + 45