1. Graphing Quadratic Functions
Math 8A & Math 8AA
2017

2. What is the graph of the parent function of a quadratic function?
The parent function of a quadratic function is in the form:
Here’s the graph of the parent function:
We call this shape a parabola.
It can open up or down.

3. Parts of quadratic functions
Y-intercept
Zeros, AKA Roots

4. Terms to know Vertex: The “turn-around” point on the graph.
When it is the top of the graph, it is called a MAXIMUM.
When it is the bottom of the graph, it is called a MINIMUM.
ZEROES, also called ROOTS, SOLUTIONS, X-INTERCEPTS: These are the points where the graph of a quadratic function crosses the x-axis. There may be 0, 1, or 2 of these for each function.

5. MORE terms to know
Y-Intercept: This is the point where the graph crosses the y-axis.
Axis of Symmetry: This is the vertical line through the x-coordinate of the vertex about which the parabola has horizontal symmetry. YOU MUST ALWAYS WRITE THIS AS A LINE, not a number: x=2; or x=0; or x=9, etc.

6. Forms of equations The STANDARD FORM is
A, B, and C are numbers. They can be integers or rational numbers.
The sign of A determines the direction the parabola opens. Positive – opens up; Negative – opens down

7. How do I find the vertex of a parabola?
To find the x-coordinate of the vertex, use this formula:
For example:
The x-coordinate of the vertex for
this equation is 1.

8. How do I find the vertex of a parabola? continued!
To find the y-coordinate of the vertex, plug the x-coordinate into the equation and solve for y.
For this example the vertex is (1, -5).

9. Axis of Symmetry
The axis of symmetry is a vertical line, so it will always be in the form of x = ____.
For the previous example, the vertex was (1, -5).
The axis of symmetry is x = 1.

10. Graphing quadratics
For this class, you will need to graph a quadratic by finding the vertex, axis of symmetry, and 2 points on either side of the vertex.
Make a t-chart and write the vertex in the middle.
From the previous example: x y 1 -5

11. Graphing quadratics
Finish by filling in the remaining spaces in the chart by picking x-values and plugging them into the equation: x y -1 19 1 -5 2 3

12. Graphing quadratics
Finish by plotting the points on a graph and connecting the dots.
Draw in the Axis of Symmetry (AoS) as a dotted line.
This graph is enlarged on the next slide.

13. Enlarged graph

14. Let’s try another one

15. Find the vertex and the axis of symmetry
The x-coordinate =
The y-coordinate =
Vertex (2, 3); Axis of Symmetry: x=2
This parabola will open DOWN because the leading coefficient is negative.

16. Find the points needed to graph the function
This is what your table looks like to start x y 2 3 x y -1 1 2 3 4
Final Table

17. Graph the function