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

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

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Q1a

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

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Q1b

Graph

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

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Q2a

Graph

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

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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)

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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)

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Q4

Determine the maximum or minimum value of

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

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Q5a

Determine the maximum or minimum value of

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

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Q5b

Determine the maximum or minimum value of

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

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Q5c

Determine the maximum or minimum value of

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

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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.

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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.

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Q7

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

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1.19mins
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.

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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.

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Q10

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

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Q11

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

a) the domain and range of f(x)

b) the equation f^{-1}

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Q12

Simplify.

\displaystyle \sqrt{48}

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Q13a

Simplify.

\displaystyle \sqrt{68}

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Q13b

Simplify.

\displaystyle \sqrt{180}

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Q13c

Simplify.

\displaystyle -3\sqrt{75}

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Q13d

Simplify.

\displaystyle 5\sqrt{98}

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Q13e

Simplify.

\displaystyle -9\sqrt{12}

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Q13f

Simplify.

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

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Q14a

Simplify.

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

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Q14b

Simplify.

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

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Q14c

Simplify.

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

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0.40mins
Q14d

Simplify.

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

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Q14e

Simplify.

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

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Q14f