1. Graphing Quadratic Functions

2. 2 Forms of Quadratic Equations
y = ax2 + bx + c
y = a(x – h)2 + k
Standard Form
Vertex Form

3. The axis of symmetry for the parabola is the vertical line through the vertex.

4. Graphing Using Vertex Form
y = a(x – h)2 + k
Vertex: (h, k)
Axis of symmetry: x = h
VERTICAL LINE
If a is positive, then it opens up.
If a is negative, then it opens down.

5. Graphing Using Vertex Form
Find and sketch the axis of symmetry (opposite of h).
Find and plot your vertex (opposite of h, same as k).
Construct a table of values to find 2 points on one side of the axis of symmetry (choose 2 x-values above your symmetry value)

6. Graphing Using Vertex Form
Use Symmetry to plot the points on the opposite side of your axis of symmetry.
Connect them with a U-shaped curve

7. f(x)= -3(x – 2)2 + 5 a = -3 h = 2 k = 5 Opens DOWN
Tell whether it opens up or down, axis of symmetry, and name the vertex.
f(x)= -3(x – 2)2 + 5
y = a(x – h)2 + k.
a = -3
h = 2
k = 5
Opens DOWN
Axis of symmetry: x = 2
Vertex: (2, 5)

8. f(x) = (x + 4)2 – 6 k = -6 a = 1 h = -4 Opens UP
You try…
Tell whether it opens up or down, axis of symmetry, and name the vertex.
f(x) = (x + 4)2 – 6
k = -6
a = 1
h = -4
Opens UP
Axis of symmetry: x = -4
Vertex: (-4, -6)

9. OPENS UP
Graph
h = -5
k = -4 x
2(x + 5)2 - 4 y
(x, y) 

10. Graph
h = 3
k= 1
OPENS DOWN x y
(x, y) 

11. Graphing Using Standard Form
*Once it is in standard form:
Find and sketch the axis of symmetry using
Find your vertex by substituting your axis of symmetry back into the original equation and solve for y.

12. Graphing Using Standard Form
4. Construct a table of values to find 2 points on one side of the axis of symmetry (choose 2 x-values above your symmetry value)
5. Use Symmetry to plot the points on the opposite side of your axis of symmetry.
Connect them with a U-shaped curve
*Remember: If a is positive, it opens up, if a is negative, it opens down.

13. OPENS UP
Graph
a = 1
b = 8
c = 13 x
(x)2 + 8x + 13 y
(x, y) 

14. Graph
a = -1
b = 2
c = 0
OPENS DOWN x
-(x)2 + 2x y
(x, y) 

15. Converting From Vertex Form to Standard Form:
y = (x – 3)2 + 5
Step 1: FOIL the binomial
Step 2: Multiply the “a” term by what you just foiled
Step 3: combine like terms!

16. Convert the following to standard form:
y = 2(x – 4)2 + 6

17. Convert the following to standard form:
y = (x + 3)² + 4

18. Converting From Standard Form to Vertex Form
Step 1: Identify a, b, and c
Step 2: find the vertex (h, k)
x-coordinate (h) =
y-coordinate (k) = substitute the value you found for the x coordinate.
Step 3: Substitute a, h, and k into vertex form!

19. Convert the following to vertex form:

20. What is the vertex form of a parabola whose standard form equation is:

21. Convert the following to vertex form: