Quadratic Functions
List the four transformations that occurred on the following function.
f(x)=-6(x+10)2-4
What is the period of a function?
The period is the length of the smallest interval that contains exactly one copy of the repeating pattern and can be calculated by 2pi divided by b.
How can you identify an exponential function from a table of values?
You will need to create a first and second differences table to identify this. When doing this you will realize that the differences are never constant, like they are for linear and quadratic equations but that they are multiples and related by a multiplication pattern.
Without solving determine the number of real solutions of:30x2-10x+5.
there are no real solutions
The function undergoes a reflection in the x-axis, a vertical stretch by a factor of 4, a horizontal shift to the left by 90 degrees and a vertical translation up by 4. What is the new equation?
f(x)=-4sin(x+90)+4
Julie invested $5000 in a simple interest account that earns 2.3% interest. How much interest will she earn in 20 years?
$2300
Determine the missing factor:
a) 10x(x-5)-6(x-5)=(?)(x-5)
b) 10x2-5x=5x(?)
a) (10x-6)
b) (2x-1)
State the amplitude, period, equation of axis, range and domain of the following function: f(x)=3sin(x-90)-5
Amplitude=3
Period=2 pi or 360 degrees
EOA=-5
Range: {yER l -8<y<-2}
Domain: {xER}
You want to have $50,000 in 10 years for university. How much should you invest now at 5.5% compounded quarterly, to meet this goal?
$28,955.78
Factor 24y2z+34yz+12z
2z(4y+3)(3y+2)
Solve the following triangle.
Angle A=110 degrees
Angle B=50 degrees
side b=11m
Angle C=20 degrees
side a=13.49m
side c=4.91m
In 20 years your grandfather wants to retire with $2,000,000 in savings. Your grandfathers deposits are earning 5% compounded monthly. What regular monthly deposit must your grandfather make to meet his goal at retirement?
$4865.78
John owns a garden with 80 tomato bushes. He earns an annual revenue of $100 per bush, but if her plants more bushes, the bushes will have less room resulting in less tomatoes per bush. As a result, the annual revenue per bush is reduce by $1 for each additional bush. The cost of maintaining the tomato bushes is $10 and is modelled by the function C(x)=10(80+x).
a)Determine the revenue equation, where is the number of additional bushes planted.
b)How many bushes must John plant to maximize profit?
a) R(x)=(80+x)(100-2x)
b)85 bushes
Two speed boats leave the dock at the same time. One speed boat travels 20km N45E from the dock and the second speed boat travels 15km S70W from the dock. How far apart are the two speed boats.?
9.01 km apart
Joe owns a limited-edition Michael Jordan rookie basketball card that he bought in 1984 for $300. He assumes that the card will appreciate in value by 12% each year.
a)How much will the card be worth in 5 years?
b)How long will it take for the card to triple its value?
a)$528.70
b)9.5 years