Question

Bert and Ernie are solving the inequality 2x²+5x-3 problem 3-67 when Bert has an idea. "Can't we change this into one parabola and solve our

inequality that way?", he asks.
Ernie asks, "What do you mean?"
"Can't we determine the solutions by looking at the graph of f(x)=x²+x-6?", Bert replies.

a. Where does Bert get the equation f(x)=x²+x-6?

b. Try Bert's idea. Make a sketch of the parabola and show how it can be used to solve the
original inequality.

Answer 1

Explanation:

Given equation: f(x)=x^2+x-6

The roots of the equation, set the equation equal to zero.

`x^2+x-6=0\\x^2+3x-2x-6=0\\x(x+3)-2(x+3)=0\\ (x+3)(x-2)=0\\ x=-3,2`

Therefore, the roots of the equation are x=-3 and x=2