## Calculus on a Parabola

#### 1 A general equation for a parabola is $$f(x)=Ax^2+Bx+C$$.

1. Find $$f'(x)$$ and $$f'(0)$$

2. Evaluate $$\displaystyle \int_{-h}^h f(x) \, dx$$

#### 2 Assume you have a parabola with points at $$(-h, y_0)$$, $$(0,y_1)$$, and $$(h,y_2)$$.

1. Find values for $$A$$, $$B$$, and $$C$$ in terms of $$h, y_0, y_1$$ and $$y_2$$

2. Find $$f'(x)$$ and $$f'(0)$$ in terms of $$h, y_0, y_1$$ and $$y_2$$

3. Evaluate $$\displaystyle \int_{-h}^h f(x) \, dx$$ in terms of $$h, y_0, y_1$$ and $$y_2$$