Mid Chapter Review
Chapter
Chapter 3
Section
Mid Chapter Review
Solutions 29 Videos

For the table, calculate the second differences. Determine whether the function is quadratic. Q1a

For the table, calculate the second differences. Determine whether the function is quadratic. Q1b

Graph

\displaystyle f(x) = -3(x - 2)^2 + 5 

Q2a

Graph

\displaystyle f(x) = 2(x + 4)(x -6) 

Q2b

State the vertex, the equation of the axis of symmetry, and the domain and range.

a) \displaystyle f(x) = -3(x - 2)^2 + 5 

b) \displaystyle f(x) = 2(x + 4)(x -6) 

Q3

Express each function in standard form.

a) \displaystyle f(x) = -3(x - 2)^2 + 5 

b) \displaystyle f(x) = 2(x + 4)(x -6) 

Q4

Determine the maximum or minimum value of

\displaystyle f(x) =x^2 -6x+2 

Q5a

Determine the maximum or minimum value of

\displaystyle f(x) = 2(x-4)(x+ 6) 

Q5b

Determine the maximum or minimum value of

\displaystyle f(x) = -2x^2 + 10x 

Q5c

Determine the maximum or minimum value of

\displaystyle f(x) = -2x^2 + 10x 

Q5d

The profit function for a business is given by the equation P(x) = -4x^2 + 16x -7, where x is the number of items sold, in thousands, and P(x) is dollars in thousands. Calculate the maximum profit and how many items must be sold to achieve it.

Q6

The cost per hour of funning an assembly line in a manufacturing plant is a function of the number of items produced per hour. The cost function is C(x) = 0.3x^2 -1.2x +2, where C(x) is the cost per hour in thousands of dollars, and x is the number of items produced per hour, in thousands. Determine the most economical production level.

Q7

The sum of two numbers is 16. What is the largest possible product between these numbers?

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Q8

a) Determine the equation of the inverse of the quadratic functions f(x) = x^2 -4x + 3.

b) List the domain and range of f(x) and its inverse.

c )Sketch the graph of f(x) and its inverse.

Q9

The revenue for a business is modelled by the function R(x) = -2,8(x -10)^2 + 15, where x is the number of items sold, in thousands, and R(x) is the revenue in thousands of dollars. Express the number sold in terms of the revenue.

Q10

Almost all linear function have an inverse that is a function, but quadratic functions do not. Explain why?

Q11

Graph f(x) = - \sqrt{x + 3} and determine

a) the domain and range of f(x)

b) the equation f^{-1}

Q12

Simplify.

\displaystyle \sqrt{48} 

Q13a

Simplify.

\displaystyle \sqrt{68} 

Q13b

Simplify.

\displaystyle \sqrt{180} 

Q13c

Simplify.

\displaystyle -3\sqrt{75} 

Q13d

Simplify.

\displaystyle 5\sqrt{98} 

Q13e

Simplify.

\displaystyle -9\sqrt{12} 

Q13f

Simplify.

\displaystyle \sqrt{7} \times \sqrt{14} 

Q14a

Simplify.

\displaystyle 3\sqrt{5} \times 2\sqrt{15} 

Q14b

Simplify.

\displaystyle \sqrt{12} + 2\sqrt{48}-5\sqrt{27} 

Q14c

Simplify.

\displaystyle 3\sqrt{28} - 2\sqrt{50} + \sqrt{63} -3\sqrt{18} 

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Q14d

Simplify.

\displaystyle (4- \sqrt{3})(5+2\sqrt{3}) 

\displaystyle (3\sqrt{5} + 2\sqrt{10})(-2\sqrt{5} + 5\sqrt{10})