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!