Chapter
Chapter 3
Section
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.

0.18mins
Q1a

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

State the domain and range.

0.22mins
Q1b

Graph the function.

f(x) = -3(x -2)^2 + 5.

0.49mins
Q1c

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

0.25mins
Q2a

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

Determine the coordinates of the vertex.

0.39mins
Q2b

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

State the domain and range.

0.22mins
Q2c

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

Graph the function.

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.

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 

0.25mins
Q4a

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

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

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.

1.39mins
Q5

Describe the relationship between

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

0.48mins
Q6

0.28mins
Q7

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

0.37mins
Q8a

State the domain and range of the inverse relation.

0.25mins
Q8b

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

0.10mins
Q8c

Express each number as a mixed radical in simplest form.

 \displaystyle \sqrt{98} 

0.18mins
Q9a

Express each number as a mixed radical in simplest form.

 \displaystyle -5\sqrt{32} 

0.16mins
Q9b

Express each number as a mixed radical in simplest form.

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

0.31mins
Q9c

Express each number as a mixed radical in simplest form.

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

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.

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.

0.36mins
Q11

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

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?
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?
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.

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.

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.

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.

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).

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)?

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.

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?

0.56mins
Q20b

Calculate the point(s) of intersection of

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

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?

1.42mins
Q22

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

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