1. Graphing Quadratic Functions
Algebra Chapter 10.2
Graphing Quadratic Functions

3. The STANDARD FORM of a quadratic function is:
where
a can’t be zero

4. Name the values of a, b, and c for each
quadratic function.
a _________________
b _________________
c _________________
d _________________

5. Quadratic Equation -a -c Quadratic Term Linear Term Constant Term a c
opens up
y-intercept -a
opens down +c
shifts up -c
skinny parabola
shifts down
wide parabola

6. Make a table of values and graph
Domain Range

7. 3. If you graph a quadratic function on a piece of paper and fold it down the middle, the two sides will match exactly. The line down the middle of the parabola is called the AXIS OF SYMMETRY. The two symmetric parts are mirror images of each other.
4. The VERTEX is the lowest point (minimum) of a parabola that opens up or the highest point (maximum) of a parabola that opens down.
Fold construction paper and cut a parabola. Open up to show axis of symmetry.

8. AXIS OF SYMMETRY is the vertical line
VERTEX has an x-coordinate of
Fold construction paper and cut a parabola. Open up to show axis of symmetry.
To find the y-coordinate, substitute the x value in the equation

9. Find the critical features of the quadratic below.
Vertex
Axis of Symmetry
Opens Up/Down
Opens Up
Y-intercept
(0, 4)

11. Finding Critical Features of Quadratics
Vertex
Axis of Symmetry
Opens Up/Down
Opens Up
Y-intercept
(0, 2)

12. Finding Critical Features of Quadratics
Graph x y x y
Axis of
Symmetry -3 -2 -1 1 2 3 29
x = 3 18 9 2 -3 -6
Vertex
(3,-7) -7 4 5 -6 -3

13. Find the critical features of the quadratic below.
Vertex
Axis of Symmetry
Opens Up/Down
Opens Down
Y-intercept
(0, 0)

14. Graphing Step 1: Find the axis of symmetry and the coordinates of
the vertex.
Determine if the parabola opens up or down.
Step 2: Find two other points on the parabola.
An easy point to determine is the y-intercept.
Choose a value for x on the same side of the
vertex as the y-intercept and solve for y.
Step 3: Reflect your points across the axis of symmetry
and draw the parabola.

15. Graph
Step 1:
Step 2:
Step 3:

16. Graph
Step 1:
Step 2:
Step 3:

17. Real World: Ariel fireworks follow a parabolic path.
Suppose a particular star is projected from an aerial firework at a starting height of 520 ft with an initial upward velocity of 72 ft/s. How long will it take for the star to reach its maximum height? How far above the ground will it be?
Define variables: Let h = height and t = time in seconds
Use the function:
Find the t-coordinate:
Find the h-coordinate:
Find the vertex:

18. Suppose you have 80 ft. of fence to enclose a rectangular garden
Suppose you have 80 ft. of fence to enclose a rectangular garden. Use the function
where x is the width in feet and A is the area of the garden. What width gives you the maximum gardening area? What is the maximum area?
Write function in standard form:
Find the vertex:

19. Class & Homework p. 521 (22-42 even; 44-58 even; 65-67)
You will need graph paper!!!