Critical Points of a Parabola
What is the domain of the following function?
y=-x2+3x+10
All Real Numbers
Describe the transformation of f(x)=x2 when g(x)=3x2.
It gets narrower (vertical stretch)
At a festival, pumpkins are launched with large catapults and air cannons. On one launch, the height of a pumpkin in feet above the ground after t seconds is modeled by h=20+90t-16t2
From what height was the pumpkin launched?
20 feet
Factor the following Quadratic Equation
x2-16=0
(x+4)(x-4)
Solve the following Quadratic Equation
x2-16=0
x=-4 and x=4
Mr. Short has this many children
What is 3?
What is the range of the following function?
y=3x2-12x+10
y>=-10
Describe the transformation of f(x) = x2 when g(x) = -0.25x2.
It reflects (flips) across the x-axis and widens (reflection and vertical compression).
The length of a rectangle is 7 more than the width. If the area of the rectangle is 60 square inches, what are the dimensions of the rectangle?
5 inches by 12 inches
Factor the following Quadratic Equation
x2+7x+10=0
(x+5)(x+2)
Solve the following Quadratic Equation
x2+7x+10=0
x=-5 and x=-2
What is Aladdin’s monkey friend called?
Abu
What is the vertex of the following function?
y=3x2-12x+10
(2, -10)
Describe the transformation of f(x) = x2 when g(x) = -x2 + 5
It reflects / flips across the x-axis and shifts 5 units up (reflection, translation)
At a festival, pumpkins are launched with large catapults and air cannons. On one launch, the height of a pumpkin in feet above the ground after t seconds is modeled by h=20+90t-16t2
How long was the pumpkin in the air? Round your answer to the nearest hundredth.
5.84 seconds
Factor the following Quadratic Equation
2x2-7x-15=0
(2x+3)(x-5)
Solve the following Quadratic Equation
2x2-7x-15=0
x=-3/2 and x=5
How many colors are there in the rainbow?
7
What are the increasing and decreasing intervals of the following function?
y=3x2-12x+10
Increasing: x>2
Decreasing: x<2
What's different about the transformation of f(x) = x2 between g(x) = -0.2x2 and h(x) = (-0.2x)2
g(x) reflects across the x-axis, while h(x) doesn't
h(x) is a wider graph than g(x) (horizontal stretch versus vertical compression)
A flare is lunched up with an initial velocity of 64 feet per second from the top of a 200 foot building. The equation h(t)=-16t2+64t+200 models this situation. Determine the maximum height of the flare and the time it takes to reach that maximum.
264 feet in 2 seconds
Factor the following Quadratic Equation
10x2+17x+3=0
(2x+3)(5x+1)
Solve the following Quadratic Equation
9x2-9x+2=0
x=1/3 and x=2/3
What is the largest state in America?
Alaska
What are the x-intercepts of the following function?
y=-x2+3x+10
x=-2 and x=5
These are the steps that transform the graph of y = x2 to
y = -3(x + 4)2 + 2
Stretch by factor 3, reflect across the x-axis, shift 4 units left and 2 units up
(4 transformations in 1 problem!)
At a swim meet, Janet dives from a diving board that is 20 feet high. Her position above the ware is represented by the equation y=-16x2+24x+20, where x represents the time in seconds and y represents the height above the water. After how many seconds does Janet enter the water?
2.096 seconds
The area of a rectangle is represented by the equation 3x2+17x+10. Find the dimensions of the rectangle in terms of x.
(x+5)(3x+2)
Solve the following Quadratic Equation
2x2+5x-3=0
x=-3 and x=1/2
What is the national game of America?
Baseball