Frogs, Fleas, and Painted Cubes (Inv. 4 Intro)

Frogs, Fleas, and Painted Cubes

(Inv. 4 Intro)

Open Ended

What do you remember about quadratic functions?

Think about their graphs, tables, and equations.

Graphs

• Parabola (U-shape)

• Maximum/minimum point

• x-intercepts

• y-intercept

• axis of symmetry

Multiple Choice

Example Question the answer is b.

• A

• B

• C

• D

Multiple Select

Multi Select. The answer is A..... and D

• A

• B

• C

• D

Multiple Choice

What is a Parabola?

• The graph of a quadratic function

• The graph of a linear function

• The graph of an absolute value function

• A boat

Multiple Choice

Does this parabola have a maximum or minimum?

• Maximum

• Minimum

Multiple Choice

Does this quadratic function have a minimum or a maximum point?

• minimum point

• maximum point

• both

Multiple Choice

What is the minimum point of this quadratic function?

• (1,-4)

• (1,4)

• (-1,-4)

• (-4,-1)

Multiple Choice

What is the maximum value of the quadratic shown?

• 3

• 5

• -2

• 4

Multiple Choice

What is the vertex of the quadratic function shown?

• (5, 5)

• (-5, -5)

• (2, 0)

• (0, -2.5)

Multiple Choice

Does this parabola have a minimum or maximum and what is its value?

• minimum: 2

• maximum: 2

• minimum: 5

• maximum: 5

Multiple Choice

What is the vertex of this parabola?

• (−1, 3)

• (−3, 11)

• (−2, 5)

• (0, 5)

Multiple Choice

What is the axis of symmetry?

• the slope of the graph

• the dividing line for a parabola

• a way to spin my pencil

• the x-axis

Multiple Choice

What is the equation for axis of symmetry?

• y=3

• x=3

• x=5

• x=1

Multiple Select

Which of the following are true about the quadratic function shown? (You can choose more than one answer)

• There are two roots

• the axis of symmetry is at x = -2

• the vertex is a maximum

• the vertex is (-2, 0)

Multiple Choice

What are the green dots called?

• axis of symmetry

• vertex

• parabola

• roots or x-intercepts

Multiple Choice

What are the x-intercepts of the quadratic function shown?

• (-3,0) and (1,0)

• (0,-3) and (0,1)

Multiple Choice

What are the x- intercepts?

• x= 0 and x= -4

• x= 0 and x= 4

• y= 0

• x= 2

Multiple Choice

Use the graph to determine the solutions.

• -1 and -3

• 1 and -3

• 1 and 3

• -1 and 3

Multiple Choice

What is the y-intercept of this parabola?

• (−1, 3)

• (−3, 11)

• (−2, 5)

• (0, 5)

Multiple Choice

What is the y-intercept of this quadratic function?

• (0,3)

• (0,-3)

• (-3,0)

• (3,0)

Multiple Choice

What is the y-intercept of the quadratic function?

• 2

• 4

• -2

• 0

Quadratic Tables

• Values mirror each other

• Increase and decrease

• Second difference pattern

Multiple Choice

Determine if the table is Linear, Quadratic or other.

• Linear

• Quadratic

• Other

Multiple Choice

Determine if the table is Linear, Quadratic or other.

• Linear

• Quadratic

• Other

Multiple Choice

Which differences identify a quadratic function?

• First Differences

• Second Differences

• Third Differences

• Fourth Differences

Multiple Choice

What is the correct second difference?

• 88

• 16

• -16

• 8

Multiple Choice

Which table indicates a quadratic function?

• Table #1

• Table #2

• Table #3

Multiple Choice

What is the 2nd difference for the quadratic function represented in the table?

• -6

• 6

• -18

• 18

Multiple Choice

True or False? The table represents a quadratic function.

• True

• False

Multiple Choice

This is an example of a quadratic relation. Calculate its second differences.

• -4

• 7

• -7

• 6

• -6

Multiple Choice

From a table of values, how can you tell that you have a quadratic relation?

• The first differences are all the same.

• The second differences are all the same.

• The first differences are different.

Multiple Choice

Is the table Linear, Quadratic, or Neither?

• Linear

• Quadratic

• Neither

Multiple Choice

Is the table Linear, Quadratic, or Neither?

• Linear

• Quadratic

• Neither

Multiple Choice

This table represents what kind of function?

• Linear

• Exponential Growth

• Exponential Decay

• Quadratic

Quadratic Equations

• the variable gets squared (like x²)

• can be factored (factored form)

• (x + _) (x+ _)

Multiple Choice

Standard form of a quadratic equation

• y=x²

• y=ax²+bx+c

• y=mx+b

• y=x

Multiple Choice

What is the equation for this quadratic function?

• f(x) = (x - 3)(x+ 1)

• f(x) = (x + 3)(x- 1)

Multiple Choice

Does the equation open or or down?

Y = -3x² +7x - 2

• up

• down

Multiple Choice

Does the equation have a max or min?

y = 2x² + 7x + 5

• max

• min

Multiple Choice

Factor the equation  $f\left(x\right)=x^2-8x+16$  

• f(x)=(x+4)(x+4)

• f(x)=(x-4)(x-4)
  

• f(x)=(x-8)(x-2)

• f(x)=(x+8)(x+2)

Multiple Choice

What is the factored quadratic equation in the following graph?

• ( x+ 2)(x + 6)

• x² - 8x + 12

• (x - 2)(x - 6)

• (x - 4)(x + 4)

Multiple Choice

In factored form you can see the ______ of the graph easily.

• y-intercept

• vertex

• x-intercepts

Multiple Choice

Solve for the values of x:

(x - 5)(x - 1) = 0

• (5, 0) or (1, 0)

• (-5, 0) or (-1, 0)

• (0, -5) or (0, -1)

• (0, 5) or (0, 1)

Multiple Choice

Solve for the values of x:

(x - 5)(x - 1) = 0

• (5, 0) or (1, 0)

• (-5, 0) or (-1, 0)

• (0, -5) or (0, -1)

• (0, 5) or (0, 1)