Main content

## Algebra (all content)

### Course: Algebra (all content)ย >ย 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

ยฉ 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Worked example: quadratic formula

Solving 6x²+3=2x-6 by rewriting in standard form and identifying the parameters a, b, and c, that can be used within the quadratic formula. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- Isn't the "standard form" of quadratic equations in the form, f(x) = a(x - h)2 + k? I think that I'm a little confused with the terminology here... I thought that the form that Sal was talking about here was called "general form."(18 votes)
- That would be vertex form.(38 votes)

- would standered form be considered intercept form?(17 votes)
- No, they are not the same. Intercept form is x/a+y/b=1 where a is the x intercept and b is the y intercept.(17 votes)

- I have been searching, but can not find, a video describing the process of arriving at a quadratic function. What I mean by this is for instance a question may ask one to find the function using three given points. I have seen explanations but I'm quite confident that none of them will give me as good an answer as one of Sal's videos... Help?(14 votes)
- The video I saw doesn't help at all. It doesn't mention anything at all about finding a quadratic equation. Could you post relevant comments, or give a URL please?(1 vote)

- what is discriminant for? can you give an example?(7 votes)
- The discriminant is the expression under the square root sign in the quadratic formula:

D = bยฒ - 4ac

The sign of the discriminant can be used to find the number of solutions of the corresponding quadratic equation. There are 3 cases:

โข If D > 0, we have two solutions.

โข If D = 0, we have only one solution.

โข If D < 0, we have no (real) solutions.

Ex.) How many solutions does the equation xยฒ - 5x + 2 = 0 have?

a = 1, b = -5, c = 2

D = (-5)ยฒ - 4 * 1 * 2 = 17

Because D > 0, we have two solutions.(6 votes)

- According to my poorly written precalculus textbook, f(x)=(ax^2)+bx+c is not the standard form of a quadratic equation; it's called general/common form. My textbook defines standard form as being written f(x)= (a(x-h)^2)+k where h and k can be taken as the vertex of the parabola. I also can't seem to find this h-k form of quadratic equations anywhere on this site. It also says this h-k form can be reached from completing the square, but i can't relate the completing the square video to h-k form.(5 votes)
- http://www.khanacademy.org/math/algebra/quadtratics/v/completing-the-square-3

#13 in the quadratics section of the algebra playlist.

This video refers to the h-k form as vertex form, and you will see how completing the square has a lot to do with vertex form.(6 votes)

- I'm looking for standard form ax+by=c.(3 votes)
- that is the standard form of linear equations(4 votes)

- For standard form of a quadratic, does the leading coefficient (the a term) have to be positive?(2 votes)
- A positive leading coefficient creates a graph that opens upward, and a negative leading coefficient will open downward(2 votes)

- Is

-1 ยฑ โ41*_______*

-6

equivalent to

1 ยฑ โ41*_______*

6

?

And if so, wouldn't the second example be 'more' simplified as it removes unnecessary negation?(1 vote)- Yes, they are equivalent. And, yes the 2nd version is more simplfied.(2 votes)

- Please solve:

Sum of 2 natural number is 8 and the difference of their reciprocal is 2/15. Find the nuumbers using one variable.(1 vote)- x = one number

8-x = 2nd number

The reciprocal of x = 1/x

The reciprocal of 8-x = 1/(8-x)

The difference of their reciprocals becomes: 1/x - 1/(8-x) = 2/15

Then solve the equation.

See if you can find the 2 numbers. Comment back if you get stuck. Let me know what you tried to do.(2 votes)

- what is 19 squared in standard form?(1 vote)

## Video transcript

Rewrite the equation 6x^2 + 3 = 2x - 6 in standard form and identify a, b, and c. So standard form for a quadratic equation is ax squared plus bx plus c is equal to zero. So essentially you wanna get all of the terms on the left-hand side, and then we want to write them so that we have the x terms...where their exponents are in decreasing order. So we have the x squared term and then the x term and then we have the constant term. So let's try to do this over here. So let me rewrite our original equation. We have 6x squared plus 3 is equal to 2x minus 6. So essentially we wanna get everything on the left-hand side. so I could subtract 2x from both sides, so I could subtract 2x from both sides, so let me just...I'll take one step at a time. So I can subtract 2x from both sides. And then I'll get...and I'm gonna write it in descending order for the exponents on x. So the highest exponent is x squared. So I'll write that first. 6x squared, and then we have minus 2x, and then we have plus 3 is equal to... the 2 'x's on the right cancel out...equal to negative 6. And now, to get rid of this negative 6 on the right-hand side, we can add 6 to both sides. So let's add 6 to both sides... ...and then this simplifies to 6x squared, minus 2x, plus nine is equal to...zero. So let's make sure we're already in standard form. All of our terms, our non-zero terms are on the left-hand side, we've done that. We have a zero on the right-hand side, we've done that. And, we have the x squared term first, then the x to the first power term, then the constant term. x squared, then x to the first, then the constant term. So we are in standard form. And so we can say that a is equal to 6, a is equal to 6. We could say that b is equal to, and this is key, it's not just the 2, it's the negative 2. B is equal to negative 2, 'cause notice this says plus bx, but over here we have minus 2x. So the b is a negative 2 here. B is negative 2. And then c, c is going to be, c is going to be 9.