Chapter
Chapter 4
Section
Solutions 17 Videos

Sketch a graph of each parabola. Label the coordinates of the vertex and the equation of the axis of symmetry.

\displaystyle y = x^2 - 6 

Q1a

Sketch a graph of each parabola. Label the coordinates of the vertex and the equation of the axis of symmetry.

\displaystyle y = 2(x-5)^2 

Q1b

Sketch a graph of each parabola. Label the coordinates of the vertex and the equation of the axis of symmetry.

\displaystyle y = -\frac{1}{3}(x+3)^2 + 4 

Q1c

Sketch a graph of each relation. Label the x-intercepts and the vertex.

\displaystyle y = (x-6)(x + 2) 

Q2a

Sketch a graph of each relation. Label the x-intercepts and the vertex.

\displaystyle y = -4(x-1)(x - 9) 

Q2b

Determine an equation to represent each parabola.

Q3a

Determine an equation to represent each parabola.

Q3b

Evaluate

a) 4^0

b) 5^{-1}

c) (-3)^{-3}

d) \left(\dfrac{3}{4}\right)^{-2}

Q4

The table shows the length of a spring under a specific load.

a) Use finite differences to determine whether this is a quadratic relation.

b) Make a scatter plot of the data. Draw a curve of best fit.

c) Use your curve of best fit to predict the length of the spring under a load of 8 kg

Q5

Board-feet are used to measure the total length, in feet, of boards that are 1 inch thick and 1 foot wide that can be cut from a tree to make lumber. You can use the equation l=0.011a^2-0.68a+13.31

unfinished question

1.36mins
Q6

The St. Louis Gateway Arch in St. Louis, Missouri. was built in 1005 and was designed as a catenary. which is a curve that approximates a parabola. The arch is 102 m wide and 102 m tall.

a) Sketch a graph of the arch that is symmetrical about the y-axis.

b) Label the x-intercepts and the vertex.

c) Determine an equation to model the arch.

2.21mins
Q7

When a car is traveling at a given speed, there is a minimum turn radius it can safely make. A particular car’s minimum radius can be calculated by r = 0.6s^2, where s is the speed, in kilometres per hour, and r is the turning radius, in metres. If the car uses tires with better grip, how does this affect the equation? Justify your response.

1.26mins
Q8

The maximum viewing distance on a clear day is related to how high you are above the surface of Earth. This relationship can be approximated by the formula \displaystyle h = \frac{3}{40}d^2 , where d is the maximum distance, in kilometres, and h is your height, in metres, above the ground.

a) How high do you need to be in order to see a distance of 25 km?

b) How would the formula change if you were standing on a 20 m cliff?

1.44mins
Q9

A volleyball’s height, h, in metres, above the ground after 1 seconds is modelled by the relation h = -4.9t^2 + 5t + 2.

a) Graph the relation.

b) What is the h-intercept? What does it represent?

c) How long will it take the volleyball to hit the ground? What feature on the graph models this? Explain your answer.

2.46mins
Q10

An ant colony has 5000 ants on July 1 and doubles every year. This can be expressed as N = 5000 \times 2^t, where N represents the number of ants and t represents time, in years.

a) Find the number of ants after 2, 3, 4, and 5 years.

b) What does t = 0 represent in this situation? What does t = -2 represent?

c) When were there 625 ants? Explain.

Q11

The approximate cost of operating a certain car at a constant speed is given by the formula C= 0.006(s-50)^2 + 20, for 10 \leq s \leq 130, where s is the speed, in kilometres per hour, and C is the most, in cents per kilometre. Use a graphing calculator to compare the operating costs, at different speeds, to those of a second vehicle with formula C = 0.008(s-55)^2+15

\displaystyle \begin{array}{lllll} &y = x^2 -4x \\ &y = x^2 -4x + 5 \\ &y = x^2 -4x -2 \end{array} 
b) Examine each graph and use its properties to write an equation in the form y=(x-h)^2+k.
c) What conclusions can you make about the relation y = x^2 - 4x + c for different values of 0?