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Quadratic Equations
An example of a Quadratic Equation:
Quadratic Equations make nice curves, like this one:
Name
The name Quadratic comes from "quad" meaning square, because the variable gets squared
(like x
2
).
It is also called an "Equation of Degree 2" (because of the "2" on the x)
Standard Form
The Standard Form of a Quadratic Equation looks like this:
a, b and c are known values. a can't be 0.
"x" is the variable or unknown (we don't know it yet).
Here are some more examples:
2x
2
+ 5x + 3 = 0
In this one a=2, b=5 and c=3

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x
2
− 3x = 0
This one is a little more tricky:
Where is a? Well a=1, and we don't usually write "1x
2
"
b = -3
And where is c? Well c=0, so is not shown.
5x − 3 = 0
Oops! This one is not a quadratic equation: it is missing x
2
(in other words a=0, which means it can't be quadratic)
Hidden Quadratic Equations!
So the "Standard Form" of a Quadratic Equation is
ax
2
+ bx + c = 0
But sometimes a quadratic equation doesn't look like that! For example:
In disguise
a, b and c
x
2
= 3x -1
Move all terms to left hand side
a=1, b=-3, c=1
2(w
2
- 2w) = 5
Expand (undo the brackets),
and move 5 to left
a=2, b=-4, c=-5
z(z-1) = 3
Expand, and move 3 to left
a=1, b=-1, c=-3
5 + 1/x - 1/x
2
= 0
Multiply by x
2
a=5, b=1, c=-1
Have a Play With It
Play with the "Quadratic Equation Explorer" so you can see:
the graph it makes, and
the solutions (called "roots").
How To Solve It?
The "solutions" to the Quadratic Equation are where it is equal to zero.
There are usually 2 solutions (as shown in the graph above).
They are also called "roots", or sometimes "zeros"
There are 3 ways to find the solutions:

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Quadratic Equations An example of a Quadratic Equation: Quadratic Equations make nice curves, like this one: Name The name Quadratic comes from "quad" meaning square, because the variable gets squared (like x2). It is also called an "Equation of Degree 2" (because of the "2" on the x) Standard Form The Standard Form of a Quadratic Equation looks like this: a, b and c are known values. a can't be 0. "x" is the variable or unknown (we don't know it yet). Here are some more examples: 2x2 + 5x + 3 = 0   In this one a=2, b=5 and c=3       x2 − 3x = 0   This one is a little more tricky: Where is a? Well a=1, and we don't usually write "1x2" b = -3 And where is c? Well c=0, so is not shown. 5x − 3 = 0   Oops! This one is not a quadratic equation: it is missing x2 (in other words a=0, which means it can't be quadratic) Hidden Quadratic Equations! So the "Standard Form" of a Quadratic Equation is ax2 + bx + c = 0 But sometimes a quadratic equation doesn't look like that! For example: In disguise → In Standard Form a, b and c x2 = 3x -1 Move all terms to left hand side x2 - 3x + 1 = 0 a=1, b=-3, c=1 2(w2 - 2w) = 5 Expand (undo the brackets), and move 5 to left 2w2 - 4w - 5 = 0 a=2, b=-4, c=-5 z(z-1) = 3 Expand, and move 3 to left z2 - z - 3 = 0 a=1, b=-1, c=-3 5 + 1/x - 1/x2 = 0 Multiply by x2 5x2 + x - 1 = 0 a=5, b=1, c=-1     Have a Play With It Play with the "Quadratic Equation Explorer" so you can see: the graph it makes, and the solutions (called "roots" ...
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Really useful study material!

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