Graphs and curve sketching

Complete the table of values for y = x² + x – 4

On the grid, draw the graph of y = x² + x – 4 for values of x from –3 to 2

Write down the coordinates of the turning point of the graph of y = x² + x – 4

Complete the table of values for y = x² + x – 4

On the grid, draw the graph of y = x² + x – 4 for values of x from –3 to 2

Write down the coordinates of the turning point of the graph of y = x² + x – 4

28Sketch the graph of y = x² + 2

17Here is a sketch of part of the graph of y = k^x where k is a positive constant.

The graph passes through the point with coordinates (–1, 1.5) Find the value of k.

Here are some graphs.

Each equation in the table is the equation of one of the graphs.

Complete the table of values for y = x² – 2x – 3

On the grid, draw the graph of y = x² – 2x – 3 for values of x from –2 to 4

Complete the table of values for y = x² – 2x – 3

On the grid, draw the graph of y = x² – 2x – 3 for values of x from –2 to 4

Here is the graph of y = f (x)

On the grid, draw the graph of y = −f (x)

Here is a sketch of the graph of y = sinx°

The point marked P is a turning point on the graph. The graph of y = sinx° is translated to give the graph of y = sin (x + 180)° + 4 Following the translation the point P, shown on the graph above, moves to point R.

Find the coordinates of R.

Sketch the graph of

showing the coordinates of the turning point, in terms of p, and the coordinates of the intercept with the y-axis. You must show all your working.

Here are some graphs.

Write down the letter of the graph that could have the equation

y = x² – 4

y = –x³

Sketch the graph of y = sinx° for 0 ≤ x ≤ 360

Solve the equation 2 sinx° = –1 for 0 ≤ x ≤ 360

Complete the table of values for y = x² – x

On the grid, draw the graph of y = x² – x for values of x from –2 to 3

Use your graph to find estimates for the solutions of the equation x² – x = 4

Complete the table of values for y = x² – x

On the grid, draw the graph of y = x² – x for values of x from –2 to 3

Use your graph to find estimates for the solutions of the equation x² – x = 4

19Here is the graph of y = sinx for –180 ≤ x ≤ 180

Use the graph to find estimates for the solutions of

Write down a value of x such that

Complete the table of values for y = x² – x – 2

On the grid, draw the graph of y = x² – x – 2 for values of x from −2 to 3

Here are five graphs.

The table shows the equations of these graphs.

Match the letter of each graph with its equation.

Complete the table of values for y = 6x − x³

On the grid, draw the graph of y = 6x − x³ for values of x from −3 to 3

The diagram shows a sketch of part of the curve with equation y = cosx° P is a minimum point on the curve. Write down the coordinates of P.

Complete the table of values for y = x² − 3x + 1

On the grid, draw the graph of y = x² − 3x + 1 for values of x from −1 to 4

Using your graph, find estimates for the solutions of the equation x² − 3x + 1 = 0

Complete the table of values for y = x² − 3x + 1

On the grid, draw the graph of y = x² − 3x + 1 for values of x from −1 to 4

Using your graph, find estimates for the solutions of the equation x² − 3x + 1 = 0

Complete the table of values for y = x² – 2x + 2

On the grid, draw the graph of y = x² – 2x + 2 for values of x from –2 to 4

Use your graph to find estimates of the solutions of the equation x² – 2x + 2 = 4

Complete the table of values for y = x² – 2x + 2

On the grid, draw the graph of y = x² – 2x + 2 for values of x from –2 to 4

Use your graph to find estimates of the solutions of the equation x² – 2x + 2 = 4

18Here is a graph of y = sin x for 0 ≤ x 360

Using this graph, find estimates of all four solutions of

The graph of y = sin x is reflected in the x‑axis.

Write down an equation of the reflected graph.

Here is a graph of y = f(x)

On the grid, draw the graph of y = f(x – 2)

The diagram shows four graphs.

Each of the equations in the table is the equation of one of the graphs.

The diagram shows four graphs.

Each of the equations in the table is the equation of one of the graphs.

Complete the table of values for y = 5 – x³

On the grid below, draw the graph of y = 5 – x³ for values of x from –2 to 2

Complete the table of values for y = 5 – x³

On the grid below, draw the graph of y = 5 – x³ for values of x from –2 to 2

Here are six graphs.

Write down the letter of the graph that could have the equation

y = x³

Here are four graphs.

The graphs represent four different types of function f. Match each description of the function in the table to the letter of its graph.

On the grid, sketch the curve with equation y = 2^x Give the coordinates of any points of intersection with the axes.

Complete this table of values for y = x² + x – 4

x	–3	–2	–1	0	1	2	3
y		–2			–2

On the grid, draw the graph of y = x² + x – 4 for values of x from –3 to 3

Use the graph to estimate a solution to x² + x – 4 = 0

Sketch the graph of y = tan x° for 0 ≤ x ≤ 360

Complete the table of values for y = x² – x – 6

On the grid, draw the graph of y = x² – x – 6 for values of x from –3 to 3

Use your graph to find estimates of the solutions to the equation x² – x – 6 = –2

Complete the table of values for y = x² – x – 6

On the grid, draw the graph of y = x² – x – 6 for values of x from –3 to 3

Use your graph to find estimates of the solutions to the equation x² – x – 6 = –2

Brogan needs to draw the graph of y = x² + 1

Here is her graph.

Write down one thing that is wrong with Brogan’s graph.

Brogan needs to draw the graph of y = x² + 1

Here is her graph.

Write down one thing that is wrong with Brogan’s graph.

Complete the table of values for y = − 1

On the grid, draw the graph of y = − 1 for values of x from −2 to 3

Use your graph to find the value of x when y = 0.3

Here are some graphs.

In the table below, match each equation with the letter of its graph.

The equation of a curve is y = a^x A is the point where the curve intersects the y-axis.

State the coordinates of A.

The equation of circle C is x² + y² = 16

Draw a sketch of circle B.

Label with coordinates the centre of circle B and any points of intersection with the x-axis.