five question mixed review 1. what is this function: y= 3x-2 2. what is the y-intercept of the above...
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Five Question Mixed Review
1. What is this function: y= 3x-22. What is the y-intercept of the above
equation?3. Solve for x: 16 = 5x + 14. What is the slope of this equation: y= ½ x + 95. Write this equation in function notation: y = 6p - 7
Five Question Mixed Review--Key
1. Linear2. -23. 16 = 5x + 1 15 = 5x 3 = x or -1 -1 5 5 x = 3 15 = 5x4. ½5. f(p) = 6p - 7
Parabolas: Nature or by Design
Ideas?
Can you find the parabolic shapes?
Standard and Essential Questions
MM1A1b: Graph the basic functions f(x) = xn
Essential Question: Can you identify a quadratic function by its components?
Could you predict what it will look like with just 2
points?
Is the slope constant? If not, what is
it?
Does it point up
or down?
What shape? How is it
different from a linear graph?
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).
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).
This is a quadratic
parent graph.
Notice where the vertex is
located (0,0)
The equation for this graph
Is y = x2
Remember:A vertex is where the
quadratic graphturns and shifts
direction. It is also called a critical
point.
What does an input/output
chart
look like for this parent
graph?
x y
-2 4
-1 1
0 0
1 1
2 4
PonderablesWhat 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?
WhatChanged?
The vertex moved!
It moved up by one unit!
When a number is changed here, it shows how the graph moves up and down.
This quadratic graph moved
DOWN
one unit.
New vertex:
(0, -1)
Name that shift!
Name this
shift!
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?
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)
Name that shift!
What kind is it?
What is the new vertex?
Name this shift!What kind is it?
What is the new vertex?
This graph shifts both
ways!
What is the vertical shift?
What is the horizontal
shift?
What is the vertex?
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?
Identifying the Slope
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
Slope = 1
Slope = 3
Slope = 5
Slope = rise/run =
x
y
What happens if the slope is more than 1?
Slope = 4
How does it compare to the parent graph?
Slope = -4
What happened?
Slope = ½
How does this
compare to the parent
graph?
Slope = -½
How does this compare
to the last graph?
Parts of a Quadratic Equation
2)2(2 xyy- intercept
vertical shift = _2__
Slope= __2_
Horizontal shift = _2__
(Opposite of x vertex
value)
Vertex can be found at
(2, 2)
When the slope is
larger than 1 then the graph
becomes…
Graphic Organizer: Parts of a Quadratic Equation
2)2(2 xy_________
_______shift
_______
shift
(Opposite of__ vertex
value)
Vertex can be found at
(__, __)
______
Parts of a Quadratic Equation
9)6(5.0 xy
y- intercept
vertical shift= ___
Slope = ___
Horizontal shift=___
(Opposite of x vertex
value)
Vertex can be found at
(__, __)
Parts of a Quadratic Equation
3)7(2/1 xy
y- intercept
vertical shift= ___
Slope = ___
Horizontal shift=___
(Opposite of x vertex
value)
Vertex can be found at
(__, __)
When the slope is smaller than
1 then the graph
becomes…
Parts of a Quadratic Equation
44)16(56 xy
y- intercept
vertical shift= ___
Slope = ___
Horizontal shift=___
(Opposite of x vertex
value)
Vertex can be found at
(__, __)Does it matter how large the numbers are?
Get with a partner to do these!
vertexintercepty
slope33.5
vertexintercepty
slope1)1(2.4
vertexintercepty
slope4)1(.3
vertexintercepty
slope)3(.2
vertexintercepty
slope2.1
2
2
2
2
xy
xy
xy
xy
xyDirections:
Identify the
a) Slope
b) y-intercept
c) Vertex
AND
Graph 1 of these!
Partner task--Key
)3,0(vertex3intercepty
3slope33.5
)1,1(vertex1intercepty
2slope1)1(2.4
(1,4)vertex 4intercepty
1slope4)1(.3
)0,3(vertex0intercepty
1slope)3(.2
)2,0(vertex2intercepty
1slope2.1
2
2
2
2
xy
xy
xy
xy
xyDirections:
Identify the
a) Slope
b) y-intercept
c) Vertex
AND
Graph 1 of these!
Ex. y=x2-2
Quiz Graphing Quadratic Functions
1-8. Choose the function rule that matches the graph. Put the letter in the blank.
9) Which of the graphs above is the parent graph for quadratic functions? #______
10) How many graphs have a negative slope?____
2) xyA
3) 2 xyB
3)2(2
1) 2 xyC
4)5(2) 2 xyD
2)1(2) xyE
42) 2 xyF
2)3(2) 2 xyG
1)5() 2 xyH
Quiz Graphing Quadratic Functions--Key
1-8. Choose the function rule that matches the graph. Put the letter in the blank.
9) Which of the graphs above is the parent graph for quadratic functions? #___4___
10) How many graphs have a negative slope?__2__ 2) xyA
3) 2 xyB
3)2(2
1) 2 xyC
4)5(2) 2 xyD
2)1(2) xyE
42) 2 xyF
2)3(2) 2 xyG
1)5() 2 xyH
Extending/Refining
Go back to photographs
• Identify all of the parabolas you see and state whether they have a positive slope or
a negative slope!