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Quadratic
functions
Rachel Collins and Ava LaRue
Properties of Quadratics
STANDARD FORM: y=ax2 + bx + c
VERTEX FORM: y=a(x - h)2 + k
ALWAYS GRAPHS A PARABOLA:
-parent function= x2
Graphing Quadratics
Standard Form: find vertex using x= –b/2a plug that X value into a T table and
add 2 numbers below and above that value under the X column.
To find the Y value, plug in your X values to the original equation. Then plot your
points.
For example: y= x2 + 4x + 6
–4/
2(1) = -2
X
y= x2 + 4x + 6
0
(0)2 + 4(0) + 6 = 6
-1
(-1)2 + 4(-1) + 6 = 3
-2
(-2)2 + 4(-2) + 6 = 2
(-3)2 + 4(-3) + 6 = 3
-3
-4
(-4)2 + 4(-4) + 6 = 6
Graphing Quadratics
Vertex Form:
Graph the function using
transformations and using a T table.
Vertex=(h,k)
For example: y = 2(x - 1)2 + 3
Vertex:(1,5)
-use the 2 numbers below and
above the X value and plug
them into T table to find the points
Solving Quadratic Equations
FactoringSteps:
1. Set y equal to 0
2. Check for a GCF. If yes, factor it out of each number
3. Make sure it is in the form 0=ax2+bx+c
4. Find the factors of c and look for the pair that add up to b
5. You should have 2 answers for the equation
a. These answers are known as zeros, or x-intercepts
6. Example: 0=x2+3x-4
4 ,-1= (x-4)(x+1) x=4 and -1
Solving Quadratic Equations
Quadratic FormulaThe Quadratic formula is
The formula will always work when solving a quadratic equation, but you should
try and factor first
If the equation can not factor, then you must use the quadratic formula
Example: y= x2 + 4x + 6
Plug the numbers into the formula and simplify
Graphing Quadratic Inequalities
First, make sure 0 is on one side of the < or > sign
After, make a t table by finding the vertex
Next graph the equation and shade in the graph using a test point (0,0)
y< -x2 -2x +3
Vertex:(-1,4) (use -b/2a)
-use the 2 numbers below and
above the X value and plug
them into T table to find the
points
Quadratic inequalities
Make sure zero is on the other side of the inequality
Then factor to get two numbers equal to x
Set each number equal to x, solve and make a number line
x2 -4x +1< 6
x2 -4x -5< 0
(x-5)(x+1)
x=5 x=1
1<x<5
-1
5
Complex Numbers
Complex number form: a+bi
Addition: add like terms,(-2+4i)+(3-11i) = 1-7i
Subtraction: distribute “-” sign, (-2+4i)-(3-11i)= -2+4i-3+11i= -5+15i
Multiplication: multiply coefficients and add “i”s, (1+3i)(3i)= 3i+9i2 = 3i+9(-1)= 3i-9
Division: divide coefficients and subtract “i”s, 9i/3i = 3