Graphs of Functions (Edexcel IGCSE Maths A: Higher): Exam Questions

Complete the table of values for $y=x^2—x—6$

On the grid, draw the graph of $y=x^2—x—6$ for values of $x$ from $—3\mathrm{to}3$

Use your graph to find estimates of the solutions to the equation $x^2-x-6=—2$

Sketch the graph of $y=\cos x^{°}\mathrm{for}0⩽x⩽360$

The diagram shows part of a sketch of the curve $y=\sin x^{\circ }.$

Write down the coordinates of the point $P$.

Write down the coordinates of the point $Q$.

Complete the table of values for $y=x^2-3x+2$

On the grid, draw the graph of $y=x^2—3x+2$ for values of $x$ from $—1\mathrm{to}5$

Find estimates for the solutions of the equation $x^2-3x+2=4$

Complete the table of values for $y=x^2-3x+1$

On the grid, draw the graph of $y=x^2—3x+1$ for values of $x$from $—2\mathrm{to}4$

By drawing a suitable straight line on the grid, find estimates for the solutions of

$x^2-3x+1=3$

Complete the table of values for $y=x^2–5x+6$

On the grid, draw the graph of $y=x^2–5x+6\mathrm{for}0⩽x⩽5$

By drawing a suitable straight line on the grid, find estimates for the solutions of the equation

$x^2–5x=x–7$

Part of the graph of$y=2x^2-4x-1$ is shown on the grid.

Use the graph to find estimates for the solutions of the equation $2x^2-4x-1=0$

Give your solutions correct to one decimal place.

By drawing a suitable straight line on the grid, find estimates for the solutions of the equation $x^2-x-1=0$

Show your working clearly.

Give your solutions correct to one decimal place.

The diagram shows the graph of $y=\mathrm{f}\left(x\right)$ for $-4⩽x⩽12$

Note: Point P in the graph is from the previous question. It is not required for this question.

The equation $\mathrm{f}\left(x\right)=k$ has exactly two different solutions for $-4⩽x⩽12$

Use the graph to find the two possible values of $k$.

Write $3x^2-12x+7$ in the form $a{(x+b)}^2+c$

The line $\mathbf{L}$ is the line of symmetry of the curve with equation $y=3x^2-12x+7$

Using your answer to part (a) or otherwise, write down an equation of $\mathbf{L}$.

Circle the point that lies on the curve  $y=x^2–4x+1$

Here is a sketch of $y=\cos x$for values of $x$ from 0° to 360°

$\alpha °$ is an acute angle.

$\cos \alpha °=k$

Circle the value of $\cos (180°–\alpha °)$

Circle the value of $\cos$$(360°+\alpha °)$

Complete the table of values for $y=x^2–x–4$

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

Complete the table of values for $y=x^3-3x+1$

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

Here are four graphs.

Write down the letter of the graph that could have the equation $y=-\frac{1}{x^2}$

Complete the table of values for $y=x^2—2x$

On the grid, draw the graph of $y=x^2—2x$for values of $x$ from $—2\mathrm{to}4$

Solve  $x^2-2x-2=1$

Complete the table of values for $y=x^2—2x—1$

On the grid, draw the graph of  $y=x^2—2x—1$ for values of $x$ from $—2\mathrm{to}4$

Solve   $x^2-2x-1=x+3$

The diagram shows the graph of $y=x^2—4x—2$

Use the graph to find estimates for the solutions of

i) $x^2-4x-2=0$

[1]

ii) $x^2-4x-6=0$

[2]

Use the graph to find estimates for the values of $x$ that satisfy the simultaneous equations

$\begin{array}{rcl}y& =& x^2—4x—2\\ & & \\ x+y& =& 6\end{array}$

Complete the table of values for $y=x^3–2x^2–3x+4$

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

By drawing a suitable straight line on the grid, find estimates for the solutions of the equation $x^3–2x^2–x+1=0$

Give your solutions correct to 1 decimal place.

The curve $\mathit{C}$has equation $y=4{(x-1)}^2-a$   where $a>4$

Using the axes below, sketch the curve $\mathit{C}$. On your sketch show clearly, in terms of $a$,

(i) the coordinates of any points of intersection of $\mathit{C}$ with the coordinate axes,

(ii) the coordinates of the turning point.

Express $7+12x–3x^2$ in the form $a+b{(x+c)}^2$ where $a,b$ and$c$are integers.

$\mathbf{C}$ is the curve with equation$y=7+12x–3x^2$

The point $A$ is the maximum point on $\mathbf{C}$

Use your answer to part (a) to write down the coordinates of $A$

Complete the table of values for $y=\frac{1}{2}{x}^3–2x+3$

On the grid, draw the graph of $y=\frac{1}{2}{x}^3–2x+3\mathrm{for}–3⩽x⩽3$

By drawing a suitable straight line on the grid, find an estimate for the solution of the equation $\frac{1}{2}{x}^3–x+4=0$

$x=$............................................ 

The curve $\mathbf{C}$ has equation $y=3–5{(x+1)}^2$
The point $A$ is the maximum point on $\mathbf{C}$.

Write down the coordinates of $A$.

The curve $C$ has equation $y=x^2–6x+4$

Using the axes below, sketch the curve $C$. On your sketch show clearly

(i) the exact coordinates of any points of intersection of $C$ with the coordinate axes,

(ii) the coordinates of the turning point.

The curve $C$ has equation $y=\mathrm{f}\left(x\right)$ where $\mathrm{f}\left(x\right)=9–3{(x+2)}^2$

The point $A$ is the maximum point on $\mathbf{C}$.

Write down the coordinates of $A$.

The curve $\mathbf{C}$ is transformed to the curve $\mathbf{S}$ by a translation of $\left(\begin{array}{c}4\\ 0\end{array}\right)$ Find an equation for the curve $\mathbf{S}$.

The curve $\mathbf{C}$ is transformed to the curve $\mathbf{T}$.

The curve $\mathbf{T}$ has equation $y=3{(x+2)}^2–9$

Describe fully the transformation that maps curve $\mathbf{C}$ onto curve $\mathbf{T}$.

Write $x^2+4x-16$ in the form ${\left(x+a\right)}^2-b$.

Sketch the graph of $y=x^2+4x-16$ , showing clearly the coordinates of any turning points.

Write  $x^2-10x+22$  in the form  ${\left(x-a\right)}^2-b$.

Sketch the graph of $y=x^2-10x+22$ .

Show clearly the coordinates of any turning points and the value of the $y$-intercept.

The graph of $y=2x^2+3x-9$ is drawn below.

Use the graph to solve $2x^2+3x-9=0$.

$$\begin{gathered} x=............................\mathrm{or} \\ x=............................ \end{gathered}$$

The equation 2x² + x − 4 = 0 can be solved by finding the intersection of the graph of y = 2x² + 3x − 9  and the line y = ax + b.

(i) Find the value of a and the value of b.

$\begin{array}{rcl}a& =& .............................\\ b& =& ..............................\left[2\right]\end{array}$

(ii) Hence use the graph to solve the equation 2x² + x − 4 = 0.

x = ............................ or x = ............................[3]