Parabolas - Vertex/standard

Risk!

Rules:

1. Answer the question with your partner only- Show all work
2. If you get it right you can decide to risk, if wrong stay seated
3. If you risk one person from group stand up, no last second changing
4. Red = Minus points Black = Positive points

Multiple Choice

Which of the following shows
f(x) = x² + 12x - 2
written in vertex form?

• f(x) = (x + 6)² + 142
• f(x) = (x + 6)² - 34
• f(x) = (x + 6)² - 38
• f(x) = (x + 6)² + 34

Multiple Choice

Convert the equation y= x²-2x-5 into vertex form. 

• y= (x-1)²-6
• y= -(x-1)²-6
• y= (x+1)²-6
• y= -(x+6)²-1

Multiple Choice

Convert the equation y= x²+4x into vertex form. 

• y= (x+4)²-4
• y= (x-2)²+4
• y= (x+2)²-4
• y= (x+2)²

Multiple Choice

How does the graph of the equation compare to the graph of the parent function?

• Reflected over the x-axis and translated up 4
• Reflected over the x-axis and translated down 4
• Reflected over the x-axis and translated right 4 
• Reflected over the x-axis and translated left 4

Multiple Choice

Which of the following shows
f(x) = x² + 12x - 2
written in vertex form?

• f(x) = (x + 6)² + 142
• f(x) = (x + 6)² - 34
• f(x) = (x + 6)² - 38
• f(x) = (x + 6)² + 34

Multiple Choice

Convert to vertex form.

• y=3(x+1)² - 8
• y=3(x-1) ² - 8
• y=3(x+2)² - 8
• y=3(x-2)² - 8

Multiple Choice

Which description best fits the transformation of f(x)=x² into f(x) =(x-5)²+3 ?

• Opens up, shifts to the right 5, and shifts up 3

• Is narrow, shifts left 5 and up 3

• Shifts right 5 and down 3

• Opens down and shifts up 3

Multiple Choice

Which of the following equations best fits the graphs of the transformed function shown in red?

• $$f\left(x\right)=\left(x-1\right)^2-3$$

• $$f\left(x\right)=\left(x+3\right)^2-1$$

• $$f\left(x\right)=-\left(x-3\right)^2+1$$

• $$f\left(x\right)=\left(x-3\right)^2-1$$

Multiple Choice

Which of the equations below would most likely to fit the graph shown in red?

• $$y=-4x^2+3$$  

• $$y=0.2x^2+3$$  

• $$y=x^2+3$$  

• $$y=4x^2-3$$  

Multiple Choice

Which of the following equations best fits the graphs of the transformed function shown in red?

$$f\left(x\right)=x^2\ is\ shown\ in\ black.$$  

• $$f\left(x\right)=-3x^2$$  

• $$f\left(x\right)=\frac{1}{3}x^2-1$$  

• $$f\left(x\right)=\frac{1}{3}\left(x-1\right)^2$$  

• $$f\left(x\right)=3\left(x-1\right)^2$$  

Multiple Choice

How do you know if a parabola has a minimum vertex?

• When a is positive there is a minimum
• When a is negative there is a minimum
• When all the numbers in the equation are negative there is a minimum
• When all the numbers in the equation are positive there is a minimum

Multiple Choice

What causes the graph of y = x² to open downward?

• multiply the x² by a fraction
• multiply the x² by a decimal
• multiply the x² by a negative number
• multiply the x² by a number greater than 1

Multiple Choice

Convert to vertex form.

• y=4(x+4)² - 62
• y=4(x-4)² - 62
• y=4(x-8)² - 62
• y=4(x+8)² - 62

Multiple Choice

Convert the vertex form y = 2(x-3)² + 5 to standard form.

• y = 2x² - 12x + 5

• y = 2x² - 12x + 23

• y = 2x² - 6x + 5

• y = 2x² - 12x + 3

Multiple Choice

Given y = -3(x+4)² + 7, what is the standard form of the equation?

• y = 3x² - 24x - 41

• y = -3x² - 24x - 41

• y = -3x² + 24x - 41

• y = -3x² - 24x + 41

Multiple Choice

What is the standard form of y = 5(x+3)² - 2?

• y = 5x² + 30x - 43

• y = 5x² + 30x + 2

• y = 5x² + 30x + 43

• y = 5x² + 30x - 2

Multiple Choice

Determine the vertex of the parabola y=5(x-2)²–7

• (5, -7)

• (-2, -7)

• (2, -7)

• (-7, -2)

Multiple Choice

$$y=-3(x+5)^2-4$$  
Convert the equation from vertex form to standard form.

• y = 9x² - 15x + 21

• y = -3x² - 75x - 4

• y = 9x² + 90x + 221

• y = -3x² - 30x - 79

Multiple Choice

$$y=-\frac{2}{3}(x-9)^2-2$$  
Convert the equation from vertex form to standard form

• $$y=-\frac{2}{3}x^2-12x-52$$  

• $$y=-\frac{2}{3}x^2+12x-56$$  

• $$y=-\frac{2}{3}x^2+18x-56$$  

• $$y=-\frac{2}{3}x^2-18x+52$$  

Multiple Choice

What steps transform the graph y = x² to y = 2(x+2)² - 5?

• Compress by 2, shifted 2 units left and 5 down

• Stretch by 5, shifted 5 units left and 2 down

• Stretch by 2, shifted 2 units left and 5 down

• Compress by 5, shifted 2 units left and 2 down

Multiple Choice

What steps transform the graph y = x² to y = 2(x+2)² - 5?

• Compress by 2, shifted 2 units left and 5 down

• Stretch by 5, shifted 5 units left and 2 down

• Stretch by 2, shifted 2 units left and 5 down

• Compress by 5, shifted 2 units left and 2 down