Chapter Quadratics Review
Chapter
Chapter 3
Section
Chapter Quadratics Review
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Solutions 37 Videos

Consider the quadratic function f(x) = -(x -2)^2 + 5.

State the direction of opening, the vertex, and the axis of symmetry.

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0.18mins
Q1a

Consider the quadratic function f(x) = -(x -2)^2 + 5.

State the domain and range.

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0.22mins
Q1b

Graph the function.

f(x) = -(x -2)^2 + 5.

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0.49mins
Q1c

State the direction of opening and the zeros of the function, f(x) = 4(x - 2)(x + 6).

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0.25mins
Q2a

Consider the quadratic function f(x) = 4(x - 2)(x + 6).

Determine the coordinates of the vertex.

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0.39mins
Q2b

Consider the quadratic function f(x) = 4(x - 2)(x + 6).

State the domain and range.

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0.22mins
Q2c

Consider the quadratic function f(x) = 4(x - 2)(x + 6).

Graph the function.

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0.46mins
Q2d

Determine the equation of the axis of symmetry of the parabola with (-5, 3) and (3, 3) equally distance from the vertex on either side it.

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0.30mins
Q3

For each quadratic function, state the maximum or minimum value of where it will occur.

\displaystyle f(x) = -3(x - 4)^2 + 7

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0.25mins
Q4a

For each quadratic function, state the maximum or minimum value of where it will occur.

f(x) = 4x(x + 6)

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0.39mins
Q4b

The height, h(t), in meters, of the trajectory of a football is given by h(t) =2+ 28t -4.9t^2, where t is the time in flight, in seconds. Determine the maximum heigh of the football and the time when the height is reached.

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1.39mins
Q5

Describe the relationship between

f(x) = x^2, g(x) = \sqrt{x}, and h(x) = -\sqrt{x}.

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0.48mins
Q6

Is the inverse of a quadratic function also a function? Give a reason for your answer.

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0.28mins
Q7

Given the graph of f(x), sketch the graph of the inverse relation.

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0.37mins
Q8a

State the domain and range of the inverse relation.

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0.25mins
Q8b

Is the inverse relation a function? Why or why not?

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0.10mins
Q8c

Express each number as a mixed radical in simplest form.

\displaystyle \sqrt{98}

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0.18mins
Q9a

Express each number as a mixed radical in simplest form.

\displaystyle -5\sqrt{32}

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0.16mins
Q9b

Express each number as a mixed radical in simplest form.

\displaystyle 4\sqrt{12}-3\sqrt{48}

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0.31mins
Q9c

Express each number as a mixed radical in simplest form.

\displaystyle (3-2\sqrt{7})^2

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0.30mins
Q9d

The area of a triangle can be calculated from Heron's formula,

\displaystyle A = \sqrt{s(s-a)(s-b)(s-c)}

where a, b, and c are the side lengths and s = \frac{a + b + c}{2}. Calculate the area of a triangle with side length 5, 7, and 10. Leave your answer in simplest radical form.

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0.50mins
Q10

What is the perimeter of a right triangle with legs 6 cm and 3 cm? Leave your answer in simplest radical form.

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0.36mins
Q11

Determine the x-int of the quadratic function f(x) = 2x^2 + x - 15.

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0.29mins
Q12

The population of a Canadian city is modelled by P(t) = 12t^2 + 800t + 40 000, where t is the time in year. When t = 0, the year is 2007.

  • According to the model, what will the population be in 2020?
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0.43mins
Q13a

The population of a Canadian city is modelled by P(t) = 12t^2 + 800t + 40 000, where t is the time in year. When t = 0, the year is 2007.

  • In what year is the population predicted to be 300 000?
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1.21mins
Q13b

A rectangular field with an area of 8000 m^2 is enclosed by 400 m of fencing. Determine the dimensions of the filed to the nearest tenth of a metre.

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2.28mins
Q14

The height, h(t), of a projectile, in metres, can be modelled by the equation h(t) = 14t - 5t^2, where t is the time in seconds after the projectile is released. Can the projectile ever reach a height of 9m? Explain.

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1.07mins
Q15

Determine the values of k for which the function f(x) = 4x^2 - 3x + 2kx + 1 has two zeros. Check these value in the original equation.

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1.46mins
Q16

Determine the break-even points of the profit function P(x) = -2x^2 + 7x + 8, where x is the number of dirt bikes reduced, in thousands.

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0.50mins
Q17

Determine the equation of the parabola with roots 2 + \sqrt{3} and 2 - \sqrt{3}, and passing through the point (2, 5).

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1.54mins
Q18

Describe the characteristics that the members of the family of parabolas f(x) = a(x+ 3)^2 -4 have in common. Which member passes through the point (-2, 6)?

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0.57mins
Q19

A engineer is designing a parabolic arch. The arch must be 15 m high, and 6 m wide at a height of 8 m.

Determine a quadratic function that satisfies these conditions.

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1.17mins
Q20a

A engineer is designing a parabolic arch. The arch must be 15 m high, and 6 m wide at a height of 8 m.

What its the width of the arch at its base?

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0.56mins
Q20b

Calculate the point(s) of intersection of

f(x) = 2x^2 + 4x - 11 and g(x) = -3x + 4.

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1.17mins
Q21

The height, h(t), of a baseball, in metres, at time t seconds after it is tossed out of a window is modelled by the function h(t) = -5t^2+20t + 15. A boy shoots at the baseball with a paintball gun. The trajectory of the paintball is given by the function g(t) = 3t + 3. Will the paintball hit the baseball? If so, when? At what height will the baseball be?

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1.42mins
Q22

Will the parabola defined by f(x) = x^2 -6x + 9 intersect the line g(x) = -3x -5? Justify your answer.

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0.18mins
Q23a

Change the slope of g(x) = -3x -5 so that it will intersect the parabola f(x) = x^2 -6x + 9 in two locations.

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2.57mins
Q23b