Activity 2: Quadratic Quest: Identify the Function!

Rearranging the terms gives $$y=-4x^2+x+5$$ . Hence, this is a quadratic function where $$a=-5,\ b=1,$$ and $$c=-5.$$

Isolating $$y$$ in the equation results in $$y=\pm\sqrt[]{x+9}$$ . This shows a radical expression on the right side. Hence, this is not a quadratic function.

Simplifying the equation gives the results:

$$x\left(x-1\right)\left(x+2\right)=-2x+y$$

$$x^3+x^2-2x=-2x=y$$

$$x^3+x^2=y$$

The highest exponent is 3. So the given is not a quadratic function.

Expanding the right side of the equation gives the following results:

$$y=-2\left(x^2+8x+16\right)-5-3$$ $$y=-2x^2-16x-32-8$$

$$y=-2x^2-16x-40$$

The resulting function is quadratic.