1. Five Question Mixed Review
1. What is this function: y= 3x-2
2. What is the y-intercept of the above equation?
Solve for x: 16 = 5x + 1
What is the slope of this equation:
y= ½ x + 9
Write this equation in function notation:
y = 6p - 7

2. Five Question Mixed Review--Key
Linear -2
16 = 5x = 5x = x or
x = 3
15 = 5x
f(p) = 6p - 7

3. Parabolas: Nature or by Design
Ideas?
What on Earth is a parabola?

4. Can you find the parabolic shapes?

14. Standard and Essential Questions
MM1A1b: Graph the basic functions f(x) = xn
Essential Question: Can you identify a quadratic function by its components?
parts

15. A quick look at the shape:
So what do we notice?
Does it point up or down?
What shape? How is it different from a linear graph?
Could you predict what it will look like with just 2 points?
Is the slope constant? If not, what is it?

16. What is a parabola? KEY NOTE CARD:
A parabola is the U-shaped graph. It can be pointing up (positive slope)
or pointing down (negative slope).

17. A quick look at an equation
The most basic quadratic formula is
y = x2 it is called a
parent graph.
This means that the U shape (a parabola) is turned up and the vertex is at (0,0).

18. This is a quadratic parent graph.
The equation
for this graph
Is y = x2
This is a quadratic parent graph.
Notice where the vertex is located (0,0)
Remember:
A vertex is
where the
quadratic graph
turns and shifts direction. It is also called a critical point.

19. x y -2 4 -1 1 2 What does an input/output chart
look like for this parent graph? x y -2 4 -1 1 2
Ponderables
What do you notice?
Do x values repeat?
Do y values repeat?
What do you call an image like this?
Can you see the vertex?
What do you notice about the slope?

20. What
Changed?
The vertex moved!
When a number is changed here, it shows how the graph moves up and down.
It moved up by one unit!

21. This quadratic graph moved DOWN
one unit.
New vertex:
(0, -1)

22. Name that shift!

23. Name this shift!

24. Shifting up and down along the y-axis is called
vertical shift.
BUT you can also shift left and right along the x-axis? What is it called?

25. The new equation would look like this:
This is called a horizontal (left/right) shift. The parent graph shifted to the left 1 unit.
The new equation would look like this:
y = (x+1)2
Horizontal movement is always inside the parentheses with the x. These equations have a trick though—you move in the opposite direction!
New vertex: (-1,0)

26. Name that shift! What kind is it?
What is the new vertex?

27. Name this shift!
What kind is it?
What is the new vertex?

28. This graph shifts both ways!
What is the vertical shift?
What is the horizontal shift?
What is the vertex?

29. What is the vertical shift? What is the horizontal shift?
How about this one?
What is the vertical shift?
What is the horizontal shift?
What is the vertex?
Notice how the equation matches the vertex except for the opposite sign inside the parentheses?

30. Identifying the Slope Slope = rise/run = IT’S A FACT:
In a parent graph the vertex is at (0,0) and the slope of the FIRST reflective points are 1. The rest of the slope is VARIABLE or CHANGING H
Slope = 5
Slope = 3
Slope = 1

31. What happens if the slope is more than 1?
How does it compare to the parent graph?

32. Slope = -4
What happened?

33. How does this compare to the parent graph?
Slope = ½
How does this compare to the parent graph?

34. Slope = -½
How does this
compare
to the last graph?

35. Parts of a Quadratic Equation
Horizontal shift = _2__
(Opposite of x vertex value)
y- intercept
vertical shift = _2__
Slope= __2_
When the slope is larger than 1 then the graph becomes…
Vertex can be found at
(2, 2)

36. Graphic Organizer: Parts of a Quadratic Equation
_______
shift
(Opposite of__ vertex value)
______
_________
_______shift
Vertex can be found at
(__, __)

37. Parts of a Quadratic Equation
Horizontal shift=___
(Opposite of x vertex value)
y- intercept
vertical shift= ___
Slope = ___
Vertex can be found at
(__, __)

38. Parts of a Quadratic Equation
Horizontal shift=___
(Opposite of x vertex value)
y- intercept
vertical shift= ___
Slope = ___
When the slope is smaller than 1 then the graph becomes…
Vertex can be found at
(__, __)

39. Parts of a Quadratic Equation
Horizontal shift=___
(Opposite of x vertex value)
y- intercept
vertical shift= ___
Slope = ___
Vertex can be found at
(__, __)
Does it matter how large the numbers are?

40. Get with a partner to do these!
Directions:
Identify the
Slope
y-intercept
Vertex
AND
Graph 1 of these!

41. Partner task--Key Ex. y=x2-2 Directions: Identify the Slope
y-intercept
Vertex
AND
Graph 1 of these!
Ex. y=x2-2

42. Quiz Graphing Quadratic Functions
Choose the function rule that matches the graph. Put the letter in the blank.
Which of the graphs above is the parent graph for quadratic functions? #______
How many graphs have a negative slope?____ 1. 5. 2. 6. 3. 7. 4. 8.

43. Quiz Graphing Quadratic Functions--Key
Choose the function rule that matches the graph. Put the letter in the blank.
Which of the graphs above is the parent graph for quadratic functions? #___4___
How many graphs have a negative slope?__2__ 1. 5. 2. 6. 3. 7. 4. 8.

44. Extending/Refining

53. Go back to photographs
Identify all of the parabolas you see and state whether they have a positive slope or a negative slope!