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# What is a quadratic equation?

By Lee Mansfield on the 11th of June, 2012

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A quadratic equation is a function with the power of 2. Meaning that the highest power of x is 2. Most of the questions asked about qiadratics is finding the x values. Quadratics can be solved by two methods: factoring or by using the quadratic formula. By factoring you can see how the quadratic breaks down into parts.

For example if the equation was x2 + 5x + 6 = 0 First step is making two sets of parentheses with an x inside

(x         )(x        ) = 0

Next step is find out what factors when multiplied give us a positive 6. Now factors of 6 are 1 * 6, and 2 * 3, but we have a positive 5 in the middle that comes from when the factors are added together,  so the only choice is 2 * 3. So we add the 2 and 3 into the parentheses to get:

(x+2)(x+3)=0

Now you solve for x, you answer is -2 and -3

A fast method is the quadratic formula, its also the only way to solve an equation if it happens to be un-factorable. So the quadratic formula is:

x = -b +/- (sqroot( b2 - 4ac)/ 2a) Where the values come from the general quadratic function ax2 + bx + c = 0

By Lini on the 22nd of January, 2013

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A quadratic equation is any equation where the highest power is 2 ( notated as x2 ).For example both  x2 =0 and 4x2 + 3x - 19 =0 are quadratic equations. Written without given variables the equation looks like this: ax2 + bx + c = 0.  One way to solve these types of problems is using the method called the quadratic formula, which is:

Remember that a.b.c are numbers that are given to you in the problem. Memorize that placement of these vaules and you will be great at solving quadratic equations. When graphing these equations the shape while always look like a U, this shape is called a parabola. So you will always have 2 values for x.

By Lini on the 17th of January, 2013

To identify a quadratic equation a symbol is used, that symbol is ‘2’.

Here's an example of a quadratic equation:

2x2+5x+8=0

The squared symbol, highlighted in red, lets us know that the equation is a quadratic equation. Quadratic comes from ‘quad’ meaning square, that’s another way to identify a quadratic equation.

The standard form of a quadratic equation is:

ax2+bx+c=0

The letters a, b and c are coefficients (you will always know the value of a,b and c). a, b and c can be any value, except ‘a’ can’t be 0.

The letter x is unknown to us, and this is the value we are trying to calculate. For example,

2x2+5x+8=0

a = 2, b = 5 and c = 8

There are three methods of how to solve quadratic equations:

1. You can factor the quadratic

2. You can use the method of completing the square

3. You can use the quadratic formula

Method 3, using the formula is what we are going to use today, the formula that is always used to solve quadratic equations is:

x=-b+-√b2-4ac

2a

At first glance it looks daunting, but if you break it up then it isn’t too bad. All we do is substitute a, b and c for values and then just enter it into a calculator.

Now let's solve 5x2+6x+1=0 we just have to follow these simple steps:

1- Write out the quadratic formula

x=-b+-√b2-4ac

2a

2- Write out the quadratic equation and pick out a, b and c.

5x2+6x+1=0

a = 5, b = 6 and c = 1

3- Substitute your a, b and c values into the formula.

x=-6+-√62-4(5)(1)

2(5)

4- Simplify the areas you can.

x=-6+-√36-20 = x=-6+-√16 = x=-6+-4

10 10 10

5- This part is important, we must do two calculations as there are two possible answers for x

.x=-6-4 and we must do x=-6+4

10 10

x = -1 or -0.2

Examples

Solve 3x2+6x+9=0 using the quadratic formula.

3x2+6x+2=0

a=3, b=6 and c=2

x=-b+-√b2-4ac

2a

x=-6+-√62-4(3)(2)

2(3)

x=-6+-√36-24

x=-6+-3.46 (2d.p)

6

x=-6+3.46 = -0.42 (2d.p)        or         x=-6-3.46 = -1.58 (2d.p)

6                                                                        6

Solve 4x2+3x+5=0 using the quadratic formula.

4x2+10x+5=0

a=4, b=10 and c=5

x=-b+-√b2-4ac

2a

x=-3+-√102-4(4)(5)

2(4)

x=-3+-√100-80

8

x=-3+-4.47 (2d.p)

8

x=-3+4.47=0.18 (2d.p)         or          x=-3-4.47=0.93 (2d.p)

8                                                             8

## Follow the links below to see how this topic has appeared in past exam papers

AQA Unit 2 November 2010 (H) - Page 10, Question 14

Other Relates Topics…

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