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### Course: Algebra (all content) > Unit 9

Lesson 7: The quadratic formula- The quadratic formula
- Understanding the quadratic formula
- Using the quadratic formula
- Worked example: quadratic formula
- Worked example: quadratic formula (example 2)
- Worked example: quadratic formula (negative coefficients)
- Quadratic formula
- Using the quadratic formula: number of solutions
- Number of solutions of quadratic equations
- Proof of the quadratic formula
- Quadratic formula review
- Discriminant review
- Quadratic formula proof review

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# Quadratic formula review

The quadratic formula allows us to solve any quadratic equation that's in the form ax^2 + bx + c = 0. This article reviews how to apply the formula.

## What is the quadratic formula?

The quadratic formula says that

for any quadratic equation like:

### Example

We're given an equation and asked to solve for $q$ :

This equation is already in the form $a{x}^{2}+bx+c=0$ , so we can apply the quadratic formula where $a=-7,b=2,c=9$ :

Let's check both solutions to be sure it worked:

Yep, both solutions check out.

*Want to learn more about the quadratic formula? Check out this video.*

*Want more practice? Check out this exercise*.

## Want to join the conversation?

- Sal, How does the quadratic formula relate to business and economics?(13 votes)
- It helps in lots of ways. It can possibly predict the future path of certain things, especially if your graph is exponential.(25 votes)

- what if the equation doesn't equal zero(3 votes)
- then just subtract the non-zero number from the RHS to the LHS and make the RHS equal to zero.(17 votes)

- are there any shortcuts or patterns we can use to make calculation quicker?(4 votes)
- Not insofar as I know. The quadratic formula is the shortcut, unless you prefer grouping or something(7 votes)

- When there are two numbers in the numerator before the square root, how do I solve the problem?(5 votes)
- Can you show an example of what you mean?(3 votes)

- Can i have exra work.(3 votes)
- ok solve this: x^2 + 69x + 420 = 0(4 votes)

- I do not understand this. Can someone please explain(1 vote)
- This is a formula, so if you can get the right numbers, you plug them into the formula and calculate the answer(s). We always have to start with a quadratic in standard form: ax^2+bx+c=0. Making one up, 3x^2+2x-5=0, we see a=3, b=2, c=-5. I teach my students to start with the discriminant, b^2-4ac. Also, especially in the beginning, put the b value in parentheses so that you square a negative number if b is negative. In our example, this gives (2)^2-4(3)(-5) = 4+60=64. If I take √64 = 8. Filling out the formula, we get x=(-2±8)/(2(3)) or breaking it into the two parts x=(-2+8)/6=1 and (-2-8)/6=-10/6=-5/2. Where is the confusion? It is always hard to answer when we cannot figure out what you do understand and where you are confused.(7 votes)

- What happens when the discriminant is a negative number? If it is negative would your answer be imaginary?(2 votes)
- Yes... If the discriminant is negative, then there are 2 roots, but they are complex numbers.(4 votes)

- can you reccomend other math websites for algebra 1 and 2(3 votes)
- isn't it the square root of -112?(2 votes)
- If you are referring to the practice problem, use the "explain" link to see how to derive the solution. Compare the work in the explanation to your work to find your error.(2 votes)

- can you reccomend other math websites for algebra 1 and 2(1 vote)
- IXL is a good one, but without a login given to you by an administrator, you have to pay a membership fee.(3 votes)