1. 9.3 Graphing Quadratic Functions
Algebra
9.3
Graphing Quadratic Functions

2. CLASSIFYING EQUATIONS
y = 2x²+ 7x + 3
y = 2x + 4
What is the pattern ?
y = 5x²
y = 5x
y = x² - 4
y = x - 4
LINEAR
QUADRATIC

3. Standard Form of a Quadratic Equation
y = ax²+ bx + c (a ≠ 0)
An equation is called QUADRATIC if
it has a squared variable
There MUST be a squared variable.
There may or may not be the “middle term”
or the constant.

4. Every quadratic function has a U-shaped graph called a parabola.
vertex ● ●
vertex
The vertex of a parabola is the lowest point of a parabola that opens up and the highest point of a parabola that opens down.

5. The axis of symmetry of a parabola is the line passing through the vertex that divides the parabola into two symmetric parts.
vertex ● ●
vertex
axis of symmetry
axis of symmetry

6. Identifying a, b and c y = ax²+ bx + c (a ≠ 0) In y = 2x²+ 3x – 5 a =-5
In y = -x²- 5x + 2
a = -1
b = -5
c = 2
In y = x²- 3x
a = 1
b = -3
c =
In y = -x²+ 4
a = -1
b =
c = 4
In y = -3x²
a = -3
b =
c =

7. The effect of a on the parabola
y = x²+ 2x + 1
y = -x²+ 2x + 1
a = 1
a = -1
If a is positive
the parabola opens up
If a is negative
the parabola opens down

8. Finding the vertex In the equation y = ax²+ bx + c●
In the equation y = ax²+ bx + c
the x coordinate of the vertex
can be found using the formula:
Then substitute the x value into the original equation to find the y coordinate
In y = x²+ 4x + 8
a = 1
b = 4
c = 8
y = (-2)² + 4(-2) + 8
VERTEX: x =
y = = 4
VERTEX: (-2, 4)

9. Graphing a Quadratic Function
STEPS
Find the x coordinate of the vertex:
Draw the line of symmetry at the x-value.
Then substitute the x value to find y.
The vertex will be an ordered pair (x,y).
x =
Make an x/y table. Choose x values to the left and right of the vertex. Plot as you go.
Connect the points as a smooth curve.

10. x y Graph: y = x²- 2x - 3 = = 1 Vertex: x = y = (1)² - 2(1) – 3 = -4-1 ● ● x -3 1 -4 ● ● 2 -3 ● 3

11. x y Graph: y = -x²+ 2x - 3 = = 1 Vertex: x = y = -(1)² + 2(1) – 3 = -2● -1 -6 ● ● x -3 1 -2 2 -3 ● ● 3 -6

12. A Few together from the Homework
pg # 5 and #15

13. Homework
pg # 1-15