Quadratic Functions
Solve for x:
x2=9
X= positive or negative 3
Solve for x: 2x=8
x=3
Solve for x:
2x+3=11
x=4
Solve the equation: |x - 3| = 5
Answers: x = -2 or x = 8
Easy data and statistics: The test scores of 7 students are: 85, 90, 85, 95, 100, 85, and 90
What is the mode of the test scores?
85
Medium quadratic: Describe the transformations of this function: g(x)=-3(x+4)2+8
1.Reflection over x-axis
2.Vertical stretch by a factor of 3
3.Shift left by 4 units
4. Shift up by 8 units
The population of a town is modeled by the function P(t)=5000(1.06)t with t representing time in years.
What will the population be after 5 years?
About 6691
Solve for x:
3(x - 2) + 4 = 2x + 7
x=9
Solve for x:
|2x-5|=9
x=7 or x=-2
In a reading challenge:
4 students read 3 books on weekdays and 2 books on weekends
3 students read 2 books on weekdays and 4 books on weekends.
2 students only read on weekends, finishing 5 books each.
Part A.) How many books were read on weekdays?
Part B.) How many books were read in total?
Part A.) 18
Part B.) 48
Find the vertex of the function
h(x)=-16x2+32x+5
(1,21)
A car's value depreciates according to the function V(t)= 20,000(0.85)t with t representing time in years
In dollars, how much will the value have decreased after 4 years?
$9,560
Solve for x:
4(x + 1) = 2x + 10
x=3
Solve for x:
|2x-1|=7
x=4 or x=-3
The amount of people in a department store was recorded for 8 different locations.
72,85,90,78,92,88,85,85
Find the median and mean (rounded to the nearest hundredth)
Median: 85
Mean:84.37
Put this into factored form:
2x2+7x+3=0
(x+3)(2x+1)=0
Solve for x: 52x+1 = 125x-1
x=4
Solve for x:
5x - (2x + 4) = 3x + 2
No solutions
Solve for x:
|3x+2|=2x+5
x=3 or x=-7/5
A class took a math quiz, and the scores were: 6,8,7,9,10,6,7,8,5,10
What is the mean score?
What is the median score?
What is the mode?
Mean: 7.6
Median: 7.5
Mode: Multiple modes, 6,7,8, and 10
Range: 5
Hard Quadratic: A soccer ball is kicked into the air from the ground. Its height in feet after t seconds is modeled by the equations. h(t)=-16t^2+40t
Part A: What is the maximum height the ball reaches, and how long does it take to reach that height?
Part B: After how many seconds does the ball hit the ground?
Maximum height: 25 feet
Time to get to Maximum height: 1.25 seconds
Time to hit the ground: the ball hits the ground after 2.5 seconds
A new app has 100 downloads on day 1. The number of downloads doubles every day.
Part A:Write a function to show the number of downloads after t days.
Part B: How many downloads will there be after 7 days, and after how many days will the downloads be more than 25,000?
Equation- D(t)=100(2)t
Downloads after 7 days: 12,800 downloads
More than 25,000 downloads after: 8 days
A company charges a setup fee plus a monthly fee for a software subscription. Another company charges a different setup fee and monthly rate.
Company A charges a setup fee of $4 and a monthly fee of $2
Company B charges a setup fee of $3 and a monthly fee of $4
For how many months will both companies charge the same total amount?
They will cost the same after half a month.
Hard absolute value: A store expects a delivery truck to arrive at 2:00PM. The delivery can be early or late by 15 minutes.
Part A: Write an absolute value equation that represents the problem
Part B: What is the earliest and latest time the truck could arrive?
Equation: |x|≤15
Earliest arrival: 1:45PM
Latest arrival:2:15PM
Medium data and statistics: The scores on a math quiz for 8 students were: 72,85,90,88,72,95,78,85
Find all the quartile ranges of the data (Q1, Q3, and IQR)
What is the range of the score?
Q1=75
Q3=89
IQR=14