IM Alg2.3.16 Lesson: Solving Quadratics

The expression is equivalent to . Which expressions are equivalent to for some number?

Elena and Han solved the equation in different ways. Elena said, “First I added 2 to each side:

So that tells me:

I can find the square roots of both sides:

Which is the same as:

So the two solutions are

and

. Han said, “I used the quadratic formula:

Since

, that means

, and

. I know:

So:

I think the solutions are

and

". Do you agree with either of them? Explain your reasoning.

Under what circumstances would solving an equation of the form lead to a solution that doesn’t involve fractions?

Solve each quadratic equation with the method of your choice. Be prepared to compare your approach with a partner‘s.