Algebra With Quadratic Functions
The solution to the equation x2+4x=21
x=-7
x=3
Identify the x and y-intercepts of the graph.
x= -1
x= 2
y=-4
Since 1972, the use of public transit - subways, buses, commuter rail, etc - in America has steadily increased. In 1972, Americans took 6.57 billion trips on public transit. By 2013, that number had risen to 10.65 billion.
By what percent has the number of trips per year increased over this time span?
62%
The population of the African country Zambia is growing continuously at a rate of about 3% per year.
In 2019, the population was 13.47 million.
Assuming this rate of growth will continue, what will Zambia’s population be in the year 2030?
18.65 Million
Factor x2-12x+36
(x-6)2
Write y=x2+6x+17 in vertex form
(x+3)2+8=y
The length of a rectangle has been increased by 120%. Meanwhile, the width of the rectangle is decreased by 60%.
What is the overall percent change to the area of the rectangle?
28%
Daily Double!!
This is worth double points.
How much money would you have to deposit in a savings account that paid 4.5% annual interest compounded monthly in order to end up with $10,000 after 8 years?
$6,993
Solve: x2-2x=15
x=5
x=-3
Identify the axis of symmetry of the parabola.
x=-3
A pair of Jordans was marked down by 10% to a sale price of $76.50.
What was the original price of the Jordans?
$85
The radioactive isotope carbon-14 is present in all living things and begins to decay as soon as the living thing dies.
By measuring how much carbon-14 remains in an object, scientists can get an idea of how old it is.
Carbon-14 decays continuously at a rate of 0.012% per year. Imagine some archaeologists are studying the bones of a woolly mammoth.
If this woolly mammoth died 25,000 years ago, then what percent of the original Carbon-14 will remain in these bones?
4.978%
Produce a different quadratics that shares a common expression with:
x2-4x-32
(x-2)2-36
or
(x-8)(x+4)
The Golden Gate Bridge connects San Francisco to Marin County. The center cable that holds up the Golden Gate Bridge forms a perfect parabola.
Your Goal: Find an equation in the form y=a(x-h)2+k that models the curve of the cable.
Your data:
- The towers are 4,200 feet apart
- The tops of the towers are 746 feet above water
-The center of the bridge is 245 feet above the water
y=(501/21002)x2+746
Write an expression that represents the following situation: increase a quantity x by 22%, then decrease this amount by 65%.
(1.22x)(0.35)
or
0.427x
Four exponential functions are graphed to the right. All are of the form y=P * Qx
Rank the functions, from smallest to largest, based on their value for P.
In other words, which functions has the smallest value for P and which has the largest?
Red
Purple
Green
Blue