This document contains information about a math class that is reviewing quadratic functions. It includes: 1. An outline of the class agenda which focuses on reviewing key concepts like how the b-value affects the parabola and completing classwork. 2. Details about grading which includes assignments, homework, tests, the final exam, and notebook checks. 3. Sample problems and class notes focused on quadratic functions, including the axis of symmetry, vertex, graphing techniques, and how changing a, b, and c values impacts the parabola. 4. Examples of completing the steps to graph quadratic functions like plotting points and reflecting over the axis of symmetry.

1. Today:
 Review from Last Week
 Getting to Know the Quadratic Function:
(how the b value changes the parabola)
 Class Work

2. Grades:
1. Class work: (20%) Ten graded assignments. How many did you
submit with all work showing?
Answers only receive no credit for those problems.
2. Home work: (20%) 15 Khan Academy Topics. How many did
you complete?
3.Tests: (40%) Six tests, lowest grade dropped. All test scores are
posted online. You can find your average test score.
4. Final Exam: (10%) This quarter's final could not hurt your
average. Everybody wins here.
5. Notebook: (10%) Is it Complete? Warm up problems? Class
notes? Is it organized? Sections labeled? Is it easy to read?
Is it a notebook full of doodles, notes to friends and folded, not
submitted class work?
Warm-Up Section of Notebook

3. Find the axis of symmetry for the graph y = 3x2
+ 6x + 4
a. y = -1 b. x = 1 c. x = -1 d. y = 1
A graph of a quadratic function has x intercepts of (3,0)
and (-7,0). Which of the following could match the graph?
a. x2
+ 4x - 21 = 0 b. x2
- 10x - 21 = 0
c. x2
+ 10x + 21 = 0 d. x2
- 4x + 21 = 0
Warm-Up/Review:

4. Warm-Up/Review:
1. y = 5x2
– 1; Graph the general shape and location from the
information given in the function. Width, shape, AOS, y-
intercept, etc. Even the missing ‘b’ term provides information.

5. Warm-Up/Review:

6. Warm-Up/Review:
Solve and graph the function: -x2
+ 2x = 1
Class Notes Section of
Notebook

7. Important Concepts to Review:
1. There is no single "right way" to graph a quadratic function.
In fact the goal is for you to understand and use a variety of
methods, so that you can choose the best (easiest) method for
a given problem.
2. The axis of symmetry is an important part of parabolas and can
save you time and effort if you understand its properties.
Because a parabola is symmetrical, two points opposite each
other on the curve are the same number of units away from
the axis of symmetry.
Helpful Hint
2.5 You must have at least 5 points to graph the parabola.

8. 4. The vertex is an (x, y) coordinate on the AOS, and is either the
minimum or maximum y value
5. All parabolas begin from the parent function (y = x2), and are moved
around the coordinate plane from changes in the a, b, and c values.
3. The axis of symmetry has a single coordinate (x) and represents the
exact center of the parabola.
6. A quadratic equation with no solutions will not cross the x-axis at
any point. It can still be graphed, however.
Important Concepts to Review:

9. How the a and c values affect the quadratic function y =
ax2 + bx + c
Start with the parent function, which is...
First, how does a change in a affect the parabola
y = x2
Review: Effects of the a, b, & c values

10. Effects of the a, b, & c values
1. The greater the value of
'a', the narrower and
steeper the graph.
2. A positive 'a' value
results in parabola which
turns up and has a vertex
minimum.
3. A negative 'a' value
results in parabola which
turns down and has a
vertex maximum.

11. Effects of the a, b, & c values
How does a change in c affect the parabola?
The value of c is also used to
find the y-intercept.
Set the 'x' values = 0, and find
the intercept.
Can we determine the equation
of this graph?

12. How changes in 'b' affect the parabola:
Why does a positive b
value (see aqua, b = 2)
result in a shift 2 units
to the left?
Effects of the a, b, & c values

13. Name five important parts of a parabola
1. Axis of Symmetry
2. Vertex
3. y-intercept
4. y-intercept translated
5. Solution(s)
How do we find each of these?
Axis of symmetry: Use the formula: -b
2aVertex:
The AOS is the x-coordinate of the vertex.
To find the y-coordinate, plug the value of
x into the equation and solve for y.
y-intercept
Write a quadratic equation in standard form: ax2 + bx + c = 0
The y-intercept is
the value of 'c' in the
quadratic equation.
y-intercept translated
Determine the distance of the y axis from
the AOS. Then, count the same distance on
the other side of the AOS. The y value will
be the same.

14. Symmetry: 5. Solution(s)
The solutions are where the graph crosses
the x-intercept.
Right now, our method for finding
solutions is by factoring.
We will be learning 3 more methods of
finding solutions:
1. By using square roots.
2. By completing the square
3. by using the quadratic function

18. Graph the quadratic function. y = x2 + 4x + 2
Step 2 Find the axis of symmetry,
Step 1: Try to picture what the graph will look like before you start.
Use the a, b, and c values to determine your prediction
Step 3: Determine the best method(s) to solve that
particular function.
Step 4 : Plot at least 5 points, then connect the dots to
complete the parabola.
then find 'y' to complete the coordinates for the vertex
Graphing Quadratic Functions: (3)

19. Step 2 Find the axis of symmetry and the vertex.
Substitute for x to find the y coordinate
The x-coordinate of the vertex is...
The y-coordinate is
Find at least 4 more points, then graph.
This is also the AOS
y = x2 + 4x + 2

20. Step 5 Graph the axis of symmetry,
the vertex, the point containing the
y-intercept, and two other points.
Step 6 Reflect the points
across the axis of symmetry.
Connect the points with a
smooth curve.
y = x2 + 4x + 2

21. STEP 1 Identify the coefficients of the function.
STEP 2 Find the vertex. Calculate the x - coordinate.
STEP 3 Draw the axis of symmetry
STEP 4 Identify the y - intercept c,
STEP 5 Find the roots by using one of the solution methods,
We are unable to find the roots with our knowledge for now, so
we'll select another value of x and solve for y. The AOS is 1, so let's
choose x = -1. Find the y coordinate.
The two other points are (–1, 10) and (–2, 25)
STEP 6 Reflect this point over the AOS to plot another point.
STEP 7 Graph the parabola
Graph a function of the form y = ax2 + bx + c
y = 3x2 – 6x + 1, Plot 5 points and draw the curveGraph

22. x = 1
(–1, 10)
(0, 1)
(1, –2)
(–2,
25)

23. Graph a function of the form y = ax2 + bx + c
Step 1: Find the axis of symmetry.
Use x = . Substitute 1 for a
and –6 for b.
The axis of symmetry is x = 3.
= 3
y = x 2 – 6x + 9 Rewrite in standard form.
y + 6x = x2 + 9Graph the quadratic function

24. Step 2: Find the vertex.
Simplify.= 9 – 18 + 9
= 0
The vertex is (3, 0).
The x-coordinate of the vertex is 3.
Substitute 3 for x.
The y-coordinate is 0.
y = x2 – 6x + 9
y = 32 – 6(3) + 9
Graph a function of the form y = ax2 + bx + c
y = x 2 – 6x + 9

25. Step 3: Find the y-intercept.
y = x2 – 6x + 9
y = x2 – 6x + 9
The y-intercept is 9; the graph passes through (0, 9).
Identify c.
Graph a function of the form y = ax2 + bx + c
y = x 2 – 6x + 9

26. Step 4 Find two more points on the same side of the axis of
symmetry as the point containing the y- intercept.
Since the axis of symmetry is x = 3, choose x-values less
than 3.
Let x = 2
y = 1(2)2 – 6(2) + 9
= 4 – 12 + 9
= 1
Let x = 1
y = 1(1)2 – 6(1) + 9
= 1 – 6 + 9
= 4
Substitute
x-coordinates.
Simplify.
Two other points are (2, 1) and (1, 4).
Graph a function of the form y = ax2 + bx + c
y = x 2 – 6x + 9

27. Step 5 Graph the axis of symmetry,
the vertex, the point containing the
y-intercept, and two other points.
Step 6 Reflect the points across
the axis of symmetry. Connect
the points with a smooth curve.
y = x 2 – 6x + 9
x = 3
(3, 0)
(0, 9)
(2, 1)
(1, 4)
(6, 9)
(5, 4)
(4, 1)
x = 3
(3, 0)

28. Class Work 4.1
~You can skip problem 2 on the back. Every other problem is required.
Be sure to show all your work for credit.
Class Work 4.2
~Find the important points on the graph. Label them, and draw the
curve.
Show your work.