1. 12.4 Quadratic Functions Goal: Graph Quadratic functions
-A Quadratic function is a polynomial with a degree of 2

2. Steps to Graph a Quadratic
Find the axis of symmetry x = -b/2a
given f(x) =ax²+bx +c
Draw your axis of symmetry as a dotted vertical line on your graph
Plug in the x value of your axis of symmetry to your quadratic equation to get your corresponding y-value to make a (x,y)
The (x,y) is your vertex (max or min point)
Your graph of a quadratic will always be a parabola (U)
If there is a negative number in front of your x² then the parabola is upside down…if it is positive then it is up
To see how wide the parabola is you can either solve for the x-intercepts by factoring and setting the factors equal to zero Or
make a xy table: pick 2 x- values to the left of the vertex and 2 x-values to the right of the vertex plug them into your function to get your corresponding y-values and graph your (x, y)

3. Steps to finding the x-intercepts (roots) of a function
Set function =0
Factor
Set each factor =0
Solve for your variable

4. Find the x-intercepts of f(x) = x2 – 5x + 6
Set the function = zero and solve.

5. Axis of Symmetry
Parabola
Model Graph
Vertex

6. Axis of Symmetry
Vertex
Model graph
Parabola

7. Graph
A = -2
B = +4
C = 1

8. Graph x y 3 -5 2 1 -1 x y 3 2 1 -1 Axis of symmetry is x= 1
Vertex: y= -2(1)² + 4(1) +1 y=
y = 3
Vertex : (1, 3) x y 3 -5 2 1 -1 x y 3 2 1 -1
X-intercepts
0 = -2x² +4 +1
0= not factorable as of now so use a xy chart

9. Domain is all real numbers
Graph x y 3 -5 2 1 -1 x y 3 2 1 -1
Domain is all real numbers
Range: { y | y }

10. Graph x y 3 2 -3 1 -4 -1 x y 3 2 1 -1
Range: { y | y }
x - intercepts

11. x y 2 4 -1
4.5 -2 -4

12. x y

13. Assignment Page 554 (2-22) even and (29-31) all