Determine whether the given below is quadratic or not. $$y=5-4x^2+x$$

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

Determine whether the given below is quadratic or not. $$y^2=x+9$$

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.

Determine whether the given below is quadratic or not. $$x\left(x-1\right)\left(x+2\right)=-2x+y$$

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.

Determine whether the given below is quadratic or not. $$y+3=-2\left(x+4\right)^2-5$$

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.

Activity 2: Quadratic Quest: Identify the Function! Flashcards

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