2.2 Quadratic Functions

​2.2 Quadratic Functions

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Multiple Choice

What do we call the graph of a quadratic function? #1

• parabola
• linear
• cubic
• sinusoidal

Multiple Choice

Does this graph have a maximum or minimum value? #3

• maximum
• minimum
• neither
• both

Multiple Choice

If given the equation y = 3(x + 5)² - 4, what is the vertex of the parabola? #2

• (5, -4)
• (-5, -4)
• (-15, -4)
• (15, -4)

Multiple Choice

Which equation best represents the graph? #6

• y = 2(x - 4)² + 5
• y = 2(x + 4)² + 5
• y = -2(x - 4)² + 5
• y = -2(x + 4)² + 5

Multiple Choice

Which answer choice describes y = -3x² +7x - 2 accurately? #7

• opens up with a maximum
• opens up with a minimum
• opens down with a maximum
• opens down with a minimum 

Multiple Choice

Find the vertex of  f(x) = -x² - 4x + 12. #8

• (-2, 16)
• (2, 0)
• (2, 4)
• (-2, 4)

Multiple Choice

What is the vertex form of a quadratic function? #16

• f(x) = 2a(x-h)² + k

• f(x) = a(x-h)² + k

• f(x) = (x+h)² + k

• f(x) = a(x-h) - k

Multiple Choice

What is the vertex form for a vertex of (-3,-5) and when a=-2? #11

• y = -2(x-3)²+5
• y = -2(x+3)²+5
• y = -2(x+3)²-5

Multiple Choice

What is the vertex of y=x²+4x+3? #13

• (2,1)
• (-2,1)
• (0,0)
• (-2,-1)

Multiple Choice

What is the y-intercept for the equation:

y = -8x² + 3x - 7 #14

• (0, -8)
• (0, 3)
• (-8, -7)
• (0, -7)

Multiple Choice

A farmer wants to construct a rectangular pigpen using 400m of fencing. The pen will be built next to an existing stone wall, so only three sides of fencing need to be constructed to enclose the pen. What dimensions should the farmer use to construct the pen with the largest possible area? #19

• 100m x 200m

• 102m x 196m

• 50m x 300m

• 50m x 175m

Multiple Choice

The height of a water balloon that is launched into the air is given by h(t) = -5x²+20x+25. When will the balloon explode on the ground? #20

• After 5 seconds

• After 1 second

• After 2 seconds

• After 3 seconds

Multiple Choice

What steps transform the graph  $$y=x^2$$   to  $$y=-\frac{1}{2}\left(x-4\right)^2+1$$ ? #30

• Compressed by 1/2, shifted 4 units right and 1 unit up

• Reflected across x-axis, compressed by 1/2, shifted 4 units right and 1 unit up

• Reflected across x-axis, stretched by 1/2, shifted 4 units left and 1 unit up

• Stretched by 1/2, shifted 4 units right and 1 unit down

Multiple Choice

If the blue is f(x)=x^2, then the red must be. #31

• g(x)=x²-5
• g(x)=x²+5
• g(x)=(x-5)²
• g(x)=(x+5)²

Multiple Choice

Given f(x) = (x-3)² + 5.  What transformations took place from the original function f(x)? #32

• Left 3 and up 5
• Right 3 and down 5
• Left 3 and down 5
• Right 3 and up 5

Multiple Choice

A kid launches a rock off of a cliff. The height of the rock after t seconds can be modeled by the graph shown. When does the rock hit the ground? #42

• 1.094 seconds

• 174.141 seconds

• 155 seconds

• 4.393 seconds

• None of the above

Multiple Choice

The function h(t) = -16t²+60t + 130 models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground? #43

• 4.2 seconds

• 4.9 seconds

• 5.3 seconds

• 5.8 seconds

• 6.1 seconds

Fill in the Blanks

After t seconds, a ball tossed in the air from the ground level reaches a height of h given by the function   $h\left(t\right)=-16t^{2\ }+144t.$  The ball hit the ground after how many seconds? (Only write the number) #50

Multiple Choice

A dolphin jumps from the water at an initial velocity of 16 feet per second. The equation h = -8t² + 16t models the dolphin's height at any given time, t. What is the maximum height the dolphin jumps? #44

• 1 foot

• 5 feet

• 7 feet

• 8 feet

• 12 feet

Fill in the Blanks

After t seconds, a ball tossed in the air from the ground level reaches a height of h given by the function  $h\left(t\right)=-16t^2+144t.$  How long did it take for the ball to reach its maximum height? (only write the number) #48

Multiple Choice

Sergei buys a rectangular rug for his living room. He measures the diagonal of the rug to be 18 feet. The length of the rug is 3 feet longer than the width. 

What are the approximate dimensions of the rug? Round each dimension to the nearest tenth of a foot. #55

• 10.4 feet by 7.4 feet

• 11.1 feet by 8.1 feet

• 13.4 feet by 10.4 feet 

• 14.1 feet by 11.1 feet

Fill in the Blanks

You have 600 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed? #56