Chapter 3.3, Problem 83AE

Answer Problems 83 and 84 using the following: A quadratic function of the form $f\left(x\right)=a{x}^2+bx+c$ with $b^2-4ac>0$ may also be written in the form $f\left(x\right)=a(x–r_1)(x-r_2)$, where $r_1\text{ and }{r}_2$ are the $x\text{-intercepts}$ of the graph of the quadratic function.

(a) Find a quadratic function whose $x\text{-intercepts}$ are $-3$ and 1 with $a=1;a=2;a=-2;a=5$.

(b) How does the value of $a$ affect the intercepts?

(c) How does the value of $a$ affect the axis of symmetry?

(d) How does the value of $a$ affect the vertex?

(e) Compare the $x\text{-coordinate}$ of the vertex with the midpoint of the $x\text{-intercepts}$. What might you conclude?