Chapter 8.2, Problem 49PE

a. Show that the points $\left(1,0\right),\left(3,10\right),$ and $\left(-2,15\right)$ are not collinear by finding the slope between $\left(1,0\right)$ and $\left(3,10\right)$ , and the slope between $\left(3,10\right)$ and $\left(-2,15\right).$ (See Example 7)

b. Find an equation of the form $y=a{x}^2+bx+c$ that defines the parabola through the points.

c. Use a graphing utility to verify that the graph of the equation in part (b) passes through the given points.