5.1
Solving Quadratic Equations by Graphing
- Quadratic Equation: y=a x 2 +bx +c
o
a,b,c R
a0
o
- Solution of Quadratic Equation
o Found by setting y=0 and finding the
- Solve means find
x -Intercepts
o
o The roots (the solutions of the equation)
o The ze
5.1
Solving Quadratic Equations by Graphing
- Quadratic Equation: y=a x 2 +bx +c
o
a,b,c R
o
a0
- Solution of Quadratic Equation
o Found by setting y=0 and finding the
- Solve means find
o
x -Intercepts
o The roots (the solutions of the equation)
o The ze
5.4
The Quadratic Formula
- i- imaginary numbers
o
i 2=1
o
i= 1
- Least Radical Form
1. 54
9 6 1
3 i6
2. 50
= 25 2 1
= 5 i2
- Quadratic Equation = a x 2+ bx+ c=0
b b24 ac
- Quadratic Formula=
2a
o You use quadratic formula to solve quadratic equations t
y=
1 2
x +3
2
Domain: cfw_ xR
Range: cfw_ yR
Vertex: ( 0,0 )
Opens: Down
Axis of Symmetry:
Max at y=3
- Given
x=0
2
y=a x 8 find a if the parabola goes through the point (3,-5).
-5= a(3 2 -8
-5= 9a-8
-5+8=9a
3=9a
a=3
4.3
Word Problems
1. The parabolic f
5.1
Solving Quadratic Equations by Graphing
- Quadratic Equation: y=a x 2 +bx +c
o
a,b,c R
a0
o
- Solution of Quadratic Equation
o Found by setting y=0 and finding the
- Solve means find
x -Intercepts
o
o The roots (the solutions of the equation)
o The ze
4.4
Graphing
2
y=a x +bx +c by Completing the Square
2
xh +k , you can tell
y =a
many things about the parabola including the vertex, axis of symmetry, and the max
or min value which you cant tell when it is in the form y=a x 2 +bx +c .
- Changing equati
5.3
Graphing Quadratic Functions by Factoring
- To graph a sketch of a quadratic equation, you need the vertex and two other
points.
- These coordinates can be found by factoring
Examples
1. y=x 28 x +12
2
0=x 8 x +12
0=( x2 )( x6 )
Axis of Symmetry
2
y=x
Chapter 4
4.1
Functions
- Relation: set of ordered pairs, (x , y )
- Function: set of ordered pairs where for every x value, there is only one y value
Function
Function
Not a Function
Not a Function
- Domain: the set of the first elements in a relation (x