1. March
18th
Today:
Warm-Up
Test Review
Khan Academy Results/Schedule
Begin Unit on Quadratic Equations

2. Khan Academy:
Saturday/Sunday -- 1409 minutes
= 23.48 Hours
Topics for March 24th:
Graphing Parabolas in Standard Form
Solving Quadratics by Factoring 1

3. Number Sense: Space & Volume

4. Number Sense: Space & Volume

5. Number Sense: Space & Volume

6. Number Sense: Space & Volume

7. Number Sense: Space & Volume
3D Sphere

8. Number Sense: Space & Volume

9. Test Review:
Top 4 missed questions from Friday's test: v.1
4th; (44% correct) #8. 32x2 = 50
3rd; (42% correct) #10. x3 - 121x = 0
2nd; (40% correct) #4. -3x3 - 12x2 = 0
1st; (37%) #3. The product of (9 - 4t)(9 + 4t) results in:

10. Quadratic Equations:
Today's Objectives:
1. Understand the characteristics of Quadratic Equations,
(What they are, and what they aren't).
2. Recognize the Graph of a Quadratic Equation
3. Describe the Differences between Quadratic & Linear
Equations
4. Solve Quadratic Equations by factoring
5. Listen Carefully, take notes, ask questions when needed.

11. Quadratic Equations:
1. What is a Quadratic Equation? From the Latin 'quad',
as in quaduplets, quadrilaterals, and quarters...
Quad means 4. A square has four sides. A variable in a
quadratic equation can have an exponent of 2, but no higher.
An exponent of 2 is a number 'squared'....
The following are all examples of quadratic equations:
x2 = 25, 4y2 + 2y - 1 = 0, y2 + 6y = 0, x2 + 2x - 4 = 0
The standard form of a quadratic is written as:
ax2 + bx + c = 0, where only a cannot = 0

12. Quadratic Equations:
We have been solving quadratic equations recently
without actually calling them Quadratics.
Let's review. Solve: x2 - 13x = 0
x( x - 13) = 0 x = 0, or x = 13
One more example. Solve: y = x2 - 4x - 5. To find the
x-intercepts, we set the equation to x2 - 4x - 5 = 0
( x - 5)( x + 1) = 0 x = 5 or x = -1
Which brings us to: What do Quadratic Equations look like
and how are they different from linear equations?

13. Linear Equations:
Y = 2x + 0 is a linear equation.
Linear Equations are straight
lines and cross the x and y axis
only one time. For each
'y', there is only one 'x'.
The greatest degree of any
exponent in a linear equation
is 1. The relationship
between x and y is constant;
the slope stays the same.

14. Linear vs. Quadratic Equations
A. The graphs of quadratics
are not straight lines, they
are always in the shape of a
Parabola.
B. Parabolas can cross an
axis more than once.
C. Unlike linear equations, each value of Y in a quadratic
equation has more than one value of x. Because Y is 0 at the
X-intercept, when we set the equation = to 0, we get the
values of the x-intercepts.
D. The slope of a quadratic is not constant. The slope-
intercept formula will not work with parabolas.

15. Parabolas: ...In Sports

16. Parabolas: ...In Archeticture

17. Parabolas: ...In Nature

18. Parabolas: ...Everywhere
Finally, the most important
Parabola of all

19. Objective 4: Solving Quadratic Equations by Factoring
There are 2 ways to factor Quadratic Equations and we
have done both already. Let's review:
Method 1: Set the equation = to 0 and solve:
Example A. x2 + 6x + 9
x2 + 6x + 9 = 0; (x + 3) (x + 3) = 0, x = -3.This is a perfect square
trinomial, and the parabola only crosses the x axis at -3 and
would be in this shape:

20. Objective 4: Solving Quadratic Equations by Factoring
Example B. x2 + 16x + 48 = 0
(x + 12) (x + 4) = 0; x = -12, x = -4. This parabola is to
the left of the Y axis
Method 2: Solve x2 = 64. Remember the standard form?
ax2 + bx + c = 0, where only a cannot = 0
In this case, b is 0, and c is 64.
We can solve by taking the square root of both sides.
The result is x = + 8; x = 8, and x = -8

21. Factoring Quadratic Equations
From the warm-up exercises, we have seen the various
ways to factor quadratic equations. The solutions, or
roots, tell us where the graph crosses the x axis.
Given this information, we can begin to plot the graph.
However, there is still more information we need to
complete the graph.

22. Graphing Parabolas & Parabola Terminology
Remember, all Quadratic Equations are in the form of
a Parabola. Parabolas are in one of these forms:
To solve and graph a quadratic
equation, we need to know where
the graph crosses the x and y axis:

23. Graphing Parabolas & Parabola Terminology
Important points on a Parabola:
1.Axis of Symmetry:The axis of symmetry is the verticle
or horizontal line which runs through the exact center
of the parabola.

24. Graphing Parabolas & Parabola Terminology
Important points on a Parabola:
2. Vertex: The vertex is the highest point (the
maximum), or the lowest point (the minimum) on a
parabola.
Notice that the axis of
symmetry always runs
through the vertex.

25. Finding the Axis of Symmetry and Vertex
1. Finding the Axis of Symmetry: The formula is: x = - b/2a
Plug in and solve for y = x2 + 12x + 32
We get - 12/2; = -6. The center of the parabola crosses the x
axis at -6. Since the axis of symmetry always runs through
the vertex, the x coordinate for the vertex is -6 also.

26. Finding the Axis of Symmetry and Vertex
There is one more point left to find and that is the
y-coordinate of the vertex. To find this, plug in the
value of the x-coordinate back into the equation and
find y. y = -12 + 12(4) + 32. Y = 1 + 48 + 32. Y = 81.
The bottom of the parabola is at -1 on the x axis, and
way up at 81 on the y axis.

29. Warm- Up Exercises
The slope is 2,
which is
positive
and the Y-
intercept
is -2
Therefore,
the
correct
graph is
A

30. Warm- Up Exercises
The Y-intercept is:0
The slope is: 2
The equation of the line is:
Y = 2x + 0
Write the equation for the line above

31. Warm- Up Exercises
3. Write the inequality for the graph below
The Y-intercept is: 2
The slope is: -3
The line is solid,
not dotted. The
equation is:
Y < -3x + 2

32. Class Work:

33. 90% of 90 girls and 80% of 110 boys have
shown up in the concert hall on time.
How many children are late?

34. Parabolas
A parabola with -x2