Author: Fabian Jauregui


Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

For example, solve for (x - 3)(x + 9) = 0.

Algebra I: 9th - 10th grade

See More

Try Our College Algebra Course. For FREE.

Sophia’s self-paced online courses are a great way to save time and money as you earn credits eligible for transfer to over 2,000 colleges and universities.*

Begin Free Trial
No credit card required

27 Sophia partners guarantee credit transfer.

245 Institutions have accepted or given pre-approval for credit transfer.

* The American Council on Education's College Credit Recommendation Service (ACE Credit®) has evaluated and recommended college credit for 21 of Sophia’s online courses. More than 2,000 colleges and universities consider ACE CREDIT recommendations in determining the applicability to their course and degree programs.



A parabola is represented by a quadratic equation. So, these types of problems can be used when trying to figure out how long it will take an object to hit the ground; or at least some type of plane. For example, assume someone is on a diving board. If they are 48 ft above the water, then how long will it take them to come in contact with the water? Similarly, if someone jumped off a building without a parachute, how long will it take them to hit the ground? So, parabolas can be used in solving these problems because objects tend to fall in the path of a curved line, or parabola.


Big Question

Now that you can find the zeros, fins the zeroes of x2 + 14x + 40 = 0