1. Quadratic Functions 4.3 - The graph of the quadratic function:
f (x) = a 𝑥 2 + bx + c.
Axis of symmetry, 𝑥=− 𝑏 2𝑎
Properties of symmetry; vertex; intercepts

2. Quadratic Function Definition
What is the difference between the Quadratic equations below?
𝑦=𝑎 𝑥 2 +𝑏𝑥+𝑐 & 𝑓 𝑥 =𝑎 𝑥 2 +𝑏𝑥+𝑐
Can both of the equations above be graphed?
How would we graph these equations?
How would these types of graphs look?
What would be the most important parts of these graphs

3. Which of these are quadratic functions?
𝑓 𝑥 =3𝑥+8−4𝑥
𝑓 𝑥 =2 𝑥 2 +8𝑥−9
𝑔 𝑥 = 𝑥 3 −9 𝑥 2 −3𝑥+6
𝑦=3 𝑥+2
ℎ 𝑥 = 3𝑥 𝑥−9
𝑠 𝑧 =(7𝑧−3)(4−𝑧)

4. Evaluating Quadratic functions
Consider the function: 𝑓 𝑥 =3 𝑥 2 +2𝑥−7
What is the value of f(x) when x = 3
What is the value of f(x) when x = 0

5. Testing solutions on Quad. Functions
Consider the function: 𝑓 𝑥 =− 1 2 𝑥 2 +2𝑥−3
Test whether the coordinate (2, 16) is a solution
Test whether these are solutions:
(4, 6)
(10, -37)
(20, -163)

6. Quadratic Function word problems
Let’s do this one on the calculator.
Steps:
Type the function into your calculator using the “y =“ button
Try to figure out how to answer questions a – c…
Take a few moments try to figure it out.

7. Graphing Quadratic Functions
All quadratic functions have a “parabola” shape to them
The vertex of a quadratic function is where the graph is at it’s mininum or maximum point
Take for instance the 𝑦= 𝑥 2 graph
to the right 
Does it have a mininum or maximum?
Is it symmetric?
If so, what is the line of symmetry?
Do you think all quadratic graphs will be
symmetric?

8. Graphing Quad. Functions (cont.)

9. Axes Intercepts
The axes are very important parts of the graphs of quadratic functions because knowing these helps us to graph the functions.

10. Y-intercepts

11. X-intercepts
In order to find the x-intercepts of a quadratic function, YOU MUST factor the function. Let’s do one, then we will write a series of steps to help us with this process:

12. X-intercepts (cont.)
Now, let’s try some that are not already factored:
Now, lets try to find the x-intercepts using technology

13. Axis of Symmetry The axis of symmetry: 𝑥=− 5 4 𝑥=−3 𝑥=4 𝑥=3 𝑥= 5 3
𝑥=−4

14. Homework in ORANGE BOOK
Pg. 503 Ex. 17A {1-5 all}
Pg. 506 Ex. 17B {1 (a,c,e), 2(a-c)}
Pg Ex. 17C {1 (a,c,e,g), 2 (a,c,e), 3 (b,d,f), 5 (a, b, d, h, j, k)}