Quadratic function problem

Question

For the quadratic function of the form y=ax^2+c for which f(1)=1 and f(2)=-2 the parameters c and a are

Answer 1

Since f(1) =1 and f(x) =ax² + c, then 1 = a + c and 1-c = a (I solved for a)

SInce f(2) = (-2) and f(x) = ax² + c, then -2 = 4a + c and (-c - 2)/4 = a (I solved for a)

Now that a is solved for in both equations, set the equations equal to each other.

1 - c = (-c - 2)/4 and now solve for c.

c = 2

Now substitue c = 2 into the equations I solve for a above.

And a = -1

Then use your calculator to graph the function f(x) = -x² + 2 and use your table of values to find f(1)=1 and f(2) = -2