Systems
How many solutions does the system have?
y = -x2 + 5x + 10
y = 0.25x + 4
2
The height in feet of a rocket after x seconds is given by the equation
y = 256x - 16x2
After how many seconds does the rocket hit the ground?
16 seconds
What is the coefficient of determination for the data set:
{(3, 16), (4, 24), (8, 9), (10, -2)}
r2 = 0.9809
A ball is thrown straight up with an initial velocity of 54ft/sec. The height of the ball t seconds after it is thrown is given by the formula f(t) = 54t - 16t2. How many seconds after the ball is thrown will it return to the ground?
Where on the graph are you looking for your answer?
positive x-intercept
This term describes a type of function in the shape of a parabola.
quadratic
y = x2 + 2x + 3
y = -5x + 3
(-7, 38) and (0, 3)
A water balloon is catapulted into the air so that its height, h, in meters, after t seconds is
h = -4.9t2 + 27t + 2.4.
How high is the balloon after 1 second?
24.5 meters
Find the equation that represents the data:
{(3, 16), (4, 24), (8, 9)}
y = -2.35x2 + 24.45x - 36.2
The function: f(x) = 2x2 - 12x + 10, models the height of a swimmer's dive off of a 10-foot platform into a pool. X represents seconds and y represents the distance above or below the surface. What is the farthest depth below the water's surface that the swimmer will reach?
Where on the graph are you looking for your answer?
y-value at minimum
This term describes multiple equations with common solutions.
System
What is the smallest y value in the solution set of the system:
y = -2x2 + 5x + 12
y = 5x + 4
-6
The function A(x) = 28x - x2, where x = width, gives you the area of a dog pen in square feet. What width gives you the maximum area?
14 feet
Use the model of best fit to predict the value of y when x = 3
{(1, 4), (2, 5), (8, -8)}
Round to nearest whole number
5
The ticket office charges x dollars for box seats for a concert. The function
S = 50x - x2 gives the estimated income from the sale of box seats. What price for box seats will maximize the income earned?
Where on the graph are you looking for your answer?
x-value at maximum
This term describes solutions that you cannot see on the graph, but do exist.
Imaginary
What is the sum of the x values in the solution set to the system:
y = x2 +2
y= x + 4
x = {-1, 2}
The sum of two numbers is 18, and the product of these two numbers is 56. What are the numbers?
4 and 14
Amery recorded the distance and height of a basketball when shooting a free throw.
{(0,4), (2,8.4), (6,12.1), (9,14.2)}
x = distance. y = height
Using the model of best fit, what is the height of the ball when it is 12 feet away?
Round to the nearest tenth13.8
(13.75692)
Suppose Ava drops a ball off the top of a 10 foot pool slide, and the ball follows the function: h(t) = -16t2 + 6, where t is the time in seconds and h is the height of the ball. Her friend Riley needs to catch the ball 2 feet above the water. After how long does she catch the ball?
Where on the graph are you looking for your answer?
x-value when y = 2
This term describes the information provided to you in a word problem that connects abstract numbers to the real world.
Context
A rocket is launched from the ground and follows a parabolic path represented by the equation y= -x2 + 10x . At the same time, a flare is launched from a height of 10 feet and follows a straight path represented by the equation y= -x + 10. x = time, y = height. When does the flare hit the rocket?
A farmer wants to make a rectangular pen for his sheep. He has 60 meters of fencing material to cover three sides with the fourth side being a brick wall. What dimensions would maximize the space for his sheep?
15 x 30
This data shows the population of a city every ten years since 1970.
{(0, 489), (10, 801), (20, 1202), (30, 1998)}
Use the model of best fit to predict the population in 2020. Round to nearest whole number.
4178
A rocket carrying fireworks is launched from a hill 80 feet above a lake. The rocket's height above the surface of the lake is given by: h(t) = -16t2 + 64t + 80. What is the height of the rocket after 3 seconds?
Where on the graph are you looking for your answer?
y-value when x = 3
This term is used to evaluate how the quadratic model best fits the provided data.
coefficient of determination