Chapter Test Quadratic Relations
Chapter
Chapter 4
Section
Chapter Test Quadratic Relations
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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

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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

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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

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Q1c

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

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

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Q2a

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

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

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Q2b

Determine an equation to represent each parabola.

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Q3a

Determine an equation to represent each parabola.

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Q3b

Evaluate

a) 4^0

b) 5^{-1}

c) (-3)^{-3}

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

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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

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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

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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.

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Q7

When a car is travelling 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.

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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?

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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.

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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.

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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

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Q12

a) Graph the following relations by developing a table of values and plotting points. Then, find the first and second differences.

\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?

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2.09mins
Q13