Quadratic Functions
Which relation is not a function?
a. {(1,2),(2,3),(3,3),(4,2)}
b. y= 2x - 9
c. x² - 5 = y²
d. y= 1
C.
When a cat is 7m from a fence, the angle of elevation to the top of the fence is 16°. What is the angle of elevation when the cat is 3m from the fence?
34°
Evaluate 265¾
64
The surface area, in square centimetres, of a cylinder with a height of 5 cm is given by the function S(r)= 2πr²+ 10πr.
a. What is the meaning of S(5) in this context?
b. Evaluate S(5)
a. S(5) represents the surface area, in square centimetres, of a cylinder with a height of 5 cm and a radius of 5 cm.
b. 314cm²
Which pairs of angles are coterminal?
a. 40° and 220°
b. 65° and 785°
c. 115° and -245°
d. -35° and -235°
a. not coterminal
b. coterminal
c. coterminal
d. not coterminal
A cubical tank at an aquarium has a capacity of 64m3. How long are its sides?
Its sides are 4m
For the graph of the quadratic function f(x)= (x - 3)² + 4, identify
a. The direction of opening
b. The coordinates of the vertex, and whether it is a maximum or a minimum value
c. The axis of symmetry
d. The y-intercept
a. upwards
b. minimum value; (3,4)
c. x= 3
d. y-intercept = 13
Two scuba divers are 100 m apart at the same depth beneath the water's surface. Their boat is located between the two divers at an angle of elevation of 60° from diver A and 54° from diver B. How far is each diver from their boat.
Diver A: approximately 89m
Diver B: approximately 95m
Bobbie has an antique piano. Middle C is tuned to a non-standard 256Hz (the international standard is 261.626 Hz). What is the frequency of a note 3 octaves below middle C on Bobbie's piano?
The frequency of a note 3 octaves below middle C is 32Hz
Determine how many real roots each equation has and then solve.
a. 2x² + 15x + 7= 0
b. 9x² - 30x + 25 = 0
c. x² + 6x + 3 = 0
D>0, so there are two real roots - 1/2 and -7
A straight tunnel is to be built through a mountain. The following measurements are taken from the endpoints, A and B, of the tunnel to a third point, C.
AC = 467.9m
BC= 634.8m
<BAC = 53.1°
How long will the tunnel be, to the nearest tenth of a metre?
The tunnel will be 515.0m
The diameter of an atom is approximately 0.000000000 1 m. Express this as a power of base 10 with a negative exponent.
10-10
Rewrite each quadratic function in vertex form y= a(x-h)²+k completing the square.
a. y=3x² - 12x +7
b.y= 1/3x² - 6x + 2
c. y= -4x² + x - 3
a. y=3(x-2)² - 5
b. y=(x-9)² - 25
c. y= -4(x - 1/8)² - 47/16
A 15m tall tree is leaning to one side. At a point 3m from the top of the tree, it is supported by an 11.5m long pole. The pole is anchored to the ground 5m from the base of the tree. At what angle is the tree leaning, relative to the vertical?
The tree is leaning 17.8°
The populations of 2 cities grow according to the exponential functions
P1(t) = 120 e 0.011 tP2(t) = 125 e 0.007 t
where P1 and P2 are the populations (in thousands) of cities A and B respectively. t is the time in years such that t is positive and t = 0 corresponds to the year 2004.
When were the populations of the two cities equal and what were their populations?
The two populations were equal in 2014.
The population in each city in 2014 was
120 e 0.011 × 10 = 134 thousand.