Chapter 8.2, Problem 50PE

a. Show that the points $\left(2,9\right),\left(-1,-6\right),$ and $\left(-4,-3\right)$ are not collinear by finding the slope between $\left(2,9\right)$ and $\left(-1,-6\right)$ , and the slope between $\left(2,9\right)$ and $\left(-4,-3\right).$

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.