Practice sheet

Fresh questions from the whole chapter, to do on paper.

New questions Include answers

To save a PDF, choose “Save as PDF” in the print dialog.

A tile pattern has 6, 9, 14 and 21 tiles in steps 1 to 4 (a square of tiles plus 5 extra). How many tiles are in step 10?
For $x = 0, 1, 2, 3, 4$ a function takes the values 5, 8, 13, 20, 29. What is the (constant) second difference?
For whole numbers $x$ from 1 to 14, which quantity is a quadratic function of $x$ ?
1. The area of a square with side $x$ cm
2. The perimeter of a square with side $x$ cm
3. The number of cells after $x$ doublings
For whole numbers $x$ from 1 to 15, which quantity is a quadratic function of $x$ ?
1. The area of a square with side $x$ cm
2. The perimeter of a square with side $x$ cm
3. The number of cells after $x$ doublings
For whole numbers $x$ from 1 to 20, which quantity is a quadratic function of $x$ ?
1. The area of a square with side $x$ cm
2. The perimeter of a square with side $x$ cm
3. The number of cells after $x$ doublings
For whole numbers $x$ from 1 to 17, which quantity is a quadratic function of $x$ ?
1. The area of a square with side $x$ cm
2. The perimeter of a square with side $x$ cm
3. The number of cells after $x$ doublings
For whole numbers $x$ from 1 to 5, which quantity is a quadratic function of $x$ ?
1. The area of a square with side $x$ cm
2. The perimeter of a square with side $x$ cm
3. The number of cells after $x$ doublings
For whole numbers $x$ from 1 to 8, which quantity is a quadratic function of $x$ ?
1. The area of a square with side $x$ cm
2. The perimeter of a square with side $x$ cm
3. The number of cells after $x$ doublings
For whole numbers $x$ from 1 to 6, which quantity is a quadratic function of $x$ ?
1. The area of a square with side $x$ cm
2. The perimeter of a square with side $x$ cm
3. The number of cells after $x$ doublings
For whole numbers $x$ from 1 to 11, which quantity is a quadratic function of $x$ ?
1. The area of a square with side $x$ cm
2. The perimeter of a square with side $x$ cm
3. The number of cells after $x$ doublings
For whole numbers $x$ from 1 to 10, which quantity is a quadratic function of $x$ ?
1. The area of a square with side $x$ cm
2. The perimeter of a square with side $x$ cm
3. The number of cells after $x$ doublings
For whole numbers $x$ from 1 to 19, which quantity is a quadratic function of $x$ ?
1. The area of a square with side $x$ cm
2. The perimeter of a square with side $x$ cm
3. The number of cells after $x$ doublings
For whole numbers $x$ from 1 to 7, which quantity is a quadratic function of $x$ ?
1. The area of a square with side $x$ cm
2. The perimeter of a square with side $x$ cm
3. The number of cells after $x$ doublings
For whole numbers $x$ from 1 to 12, which quantity is a quadratic function of $x$ ?
1. The area of a square with side $x$ cm
2. The perimeter of a square with side $x$ cm
3. The number of cells after $x$ doublings
For whole numbers $x$ from 1 to 16, which quantity is a quadratic function of $x$ ?
1. The area of a square with side $x$ cm
2. The perimeter of a square with side $x$ cm
3. The number of cells after $x$ doublings
For whole numbers $x$ from 1 to 13, which quantity is a quadratic function of $x$ ?
1. The area of a square with side $x$ cm
2. The perimeter of a square with side $x$ cm
3. The number of cells after $x$ doublings
For whole numbers $x$ from 1 to 18, which quantity is a quadratic function of $x$ ?
1. The area of a square with side $x$ cm
2. The perimeter of a square with side $x$ cm
3. The number of cells after $x$ doublings
For whole numbers $x$ from 1 to 9, which quantity is a quadratic function of $x$ ?
1. The area of a square with side $x$ cm
2. The perimeter of a square with side $x$ cm
3. The number of cells after $x$ doublings
Write $(x + 2)(x - 3)$ in standard form $ax^2 + bx + c$ .
Find the $x$ -intercepts of $y = (x - 6)(x + 2)$ .
A quadratic with leading coefficient 1 crosses the $x$ -axis at $x = 9$ and $x = -4$ . Write it in factored form.
What is the $y$ -intercept of $y = 2x^2 + 1x + 11$ ?
Does the graph of $y = -6x^2 + 5x + 2$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 2
Does the graph of $y = -5x^2 + 6x + 4$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 4
Does the graph of $y = -3x^2 + 6x + 3$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 3
Does the graph of $y = -6x^2 + 8x + 1$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 1
Does the graph of $y = -7x^2 + 7x + 1$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 1
Does the graph of $y = -7x^2 + 5x + 3$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 3
Does the graph of $y = -5x^2 + 3x + 2$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 2
Does the graph of $y = -8x^2 + 8x + 6$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 6
Does the graph of $y = -6x^2 + 3x + 5$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 5
Does the graph of $y = -5x^2 + 8x + 1$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 1
Does the graph of $y = -6x^2 + 5x + 7$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 7
Does the graph of $y = -9x^2 + 5x + 8$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 8
Does the graph of $y = -2x^2 + 3x + 2$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 2
Does the graph of $y = -4x^2 + 2x + 2$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 2
Does the graph of $y = -1x^2 + 8x + 2$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 2
Does the graph of $y = -1x^2 + 1x + 9$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 9
Does the graph of $y = -7x^2 + 8x + 2$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 2
Does the graph of $y = -2x^2 + 8x + 6$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 6
Does the graph of $y = -7x^2 + 7x + 6$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 6
Does the graph of $y = -8x^2 + 7x + 4$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 4
Does the graph of $y = -5x^2 + 3x + 9$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 9
Does the graph of $y = -8x^2 + 9x + 6$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 6
Does the graph of $y = -8x^2 + 9x + 1$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 1
Does the graph of $y = -8x^2 + 9x + 4$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 4
Does the graph of $y = -4x^2 + 9x + 6$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 6
Does the graph of $y = -8x^2 + 4x + 1$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 1
Does the graph of $y = -2x^2 + 1x + 5$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 5
Does the graph of $y = -3x^2 + 9x + 2$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 2
Does the graph of $y = -8x^2 + 1x + 3$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 3
Does the graph of $y = -6x^2 + 6x + 1$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 1
Does the graph of $y = -2x^2 + 4x + 6$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 6
Does the graph of $y = -1x^2 + 3x + 3$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 3
Does the graph of $y = -2x^2 + 6x + 9$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 9
Does the graph of $y = -3x^2 + 6x + 2$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 2
Does the graph of $y = -4x^2 + 1x + 8$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 8
Does the graph of $y = -8x^2 + 2x + 9$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 9
Does the graph of $y = -6x^2 + 5x + 5$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 5
Does the graph of $y = -7x^2 + 3x + 1$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 1
Does the graph of $y = -8x^2 + 8x + 2$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 2
Does the graph of $y = -2x^2 + 4x + 4$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 4
Does the graph of $y = -3x^2 + 4x + 7$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 7
Does the graph of $y = -9x^2 + 8x + 3$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 3
Does the graph of $y = -7x^2 + 7x + 9$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 9
Does the graph of $y = -9x^2 + 1x + 2$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 2
Does the graph of $y = -1x^2 + 5x + 7$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 7
Does the graph of $y = -5x^2 + 5x + 3$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 3
Does the graph of $y = -1x^2 + 4x + 5$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 5
Does the graph of $y = -1x^2 + 3x + 8$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 8
Does the graph of $y = -3x^2 + 3x + 2$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 2
Does the graph of $y = -9x^2 + 1x + 4$ open up or down?
1. Down, so it has a maximum
2. Up, so it has a minimum
3. It depends on 4
A parabola crosses the $x$ -axis at $x = -1$ and $x = 3$ . What is the $x$ -coordinate of its vertex?
What is the $x$ -coordinate of the vertex of $y = 3(x + 1)^2 + 4$ ?
What is the smallest value of $y = (x - 9)^2 - 3$ ?
Write a quadratic with vertex $(8, 1)$ and leading coefficient 2, in vertex form.
$f(x) = 5x^2 - 10x + 20$ . What is the $x$ -coordinate of the vertex?
$f(x) = x^2 + 10x + 21$ . What is the smallest value of $f(x)$ ?
Draw the graph of $y = -(x - h)^2 + 6$ for $h = 0$ : place the vertex and one more point.
$f(x) = \begin{cases} x + 3 & \text{if } x < 5 \\ 3x & \text{if } x \ge 5 \end{cases}$ . Find $f(5)$ .
$f(x) = \begin{cases} x + 4 & \text{if } x < 8 \\ 4x & \text{if } x \ge 8 \end{cases}$ . Find $f(0)$ .
For $x < 7$ , which expression is equal to $|x - 7|$ ?
1. $7 - x$
2. $x - 7$
3. $-x - 7$
For $x < 5$ , which expression is equal to $|x - 5|$ ?
1. $5 - x$
2. $x - 5$
3. $-x - 5$
For $x < 1$ , which expression is equal to $|x - 1|$ ?
1. $1 - x$
2. $x - 1$
3. $-x - 1$
For $x < 9$ , which expression is equal to $|x - 9|$ ?
1. $9 - x$
2. $x - 9$
3. $-x - 9$
For $x < 8$ , which expression is equal to $|x - 8|$ ?
1. $8 - x$
2. $x - 8$
3. $-x - 8$
For $x < 6$ , which expression is equal to $|x - 6|$ ?
1. $6 - x$
2. $x - 6$
3. $-x - 6$
For $x < 4$ , which expression is equal to $|x - 4|$ ?
1. $4 - x$
2. $x - 4$
3. $-x - 4$
For $x < 2$ , which expression is equal to $|x - 2|$ ?
1. $2 - x$
2. $x - 2$
3. $-x - 2$
For $x < 3$ , which expression is equal to $|x - 3|$ ?
1. $3 - x$
2. $x - 3$
3. $-x - 3$
Draw the graph of $y = (x - 1)^2 - 3$ : place the vertex and one more point.
The graph of $y = x^2$ is moved 1 units to the right and 6 units down. Write the equation of the new graph.
Match each equation with what it does to the graph of $y = f(x)$ .
1. $y = f(x) + 3$
2. $y = f(x - 3)$
3. $y = -f(x)$
4. $y = f(-x)$
1. moves it up 3 units
2. moves it 3 units to the right
3. reflects it across the x-axis
4. reflects it across the y-axis
Match each equation with what it does to the graph of $y = f(x)$ .
1. $y = f(x) + 5$
2. $y = f(x - 5)$
3. $y = -f(x)$
4. $y = f(-x)$
1. moves it up 5 units
2. moves it 5 units to the right
3. reflects it across the x-axis
4. reflects it across the y-axis
Match each equation with what it does to the graph of $y = f(x)$ .
1. $y = f(x) + 4$
2. $y = f(x - 4)$
3. $y = -f(x)$
4. $y = f(-x)$
1. moves it up 4 units
2. moves it 4 units to the right
3. reflects it across the x-axis
4. reflects it across the y-axis
Match each equation with what it does to the graph of $y = f(x)$ .
1. $y = f(x) + 2$
2. $y = f(x - 2)$
3. $y = -f(x)$
4. $y = f(-x)$
1. moves it up 2 units
2. moves it 2 units to the right
3. reflects it across the x-axis
4. reflects it across the y-axis
$f(x) = 7x + 9$ . Find $f^{-1}(x)$ .
$f(x) = 2x + 6$ . Find $f^{-1}(10)$ .
The point $(2, 7)$ is on the graph of $f$ . Tap the point that must be on the graph of $f^{-1}$ .

Answers

$105$
$2$
The area of a square with side $x$ cm
$x^{2} - x - 6$
$6,\ -2$
$\left(x - 9\right) \left(x + 4\right)$
$11$
Down, so it has a maximum
$1$
$-1$
$-3$
$2 \left(x - 8\right)^{2} + 1$
$1$
$-4$
$y = 6 - x^{2}$
$15$
$4$
$7 - x$
$y = \left(x - 1\right)^{2} - 3$
$\left(x - 1\right)^{2} - 6$
$y = f(x) + 3$ → moves it up 3 units · $y = f(x - 3)$ → moves it 3 units to the right · $y = -f(x)$ → reflects it across the x-axis · $y = f(-x)$ → reflects it across the y-axis
$\frac{x}{7} - \frac{9}{7}$
$2$
$(7, 2)$