- The quadratic formula
- Understanding the 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
- Quadratic formula review
- Discriminant 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:
We're given an equation and asked to solve for :
This equation is already in the form , so we can apply the quadratic formula where :
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.
Solve for .
Want more practice? Check out this exercise.
Want to join the conversation?
- Sal, How does the quadratic formula relate to business and economics?(9 votes)
- It helps in lots of ways. It can possibly predict the future path of certain things, especially if your graph is exponential.(19 votes)
- so maybe im just stupid but im so confused and freaking out because i might fail algebra if anyone in here has a heart to help me it would be greatly appreciated(8 votes)
- what if the equation doesn't equal zero(3 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(5 votes)
- When there are two numbers in the numerator before the square root, how do I solve the problem?(5 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.(4 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)
- What happens when the discriminant is a negative number? If it is negative would your answer be imaginary?(1 vote)