Grade 10 Maths · Functions

Find the equation of a graph

Work out the equation of a graph by choosing its general form and using given points or features to find the missing numbers.

past paper questions use it: 5 past paper questions use it
videos: 3 videos

Learn it: find the equation of a graph

Pick one and watch it, then try the questions below. Videos load only when you tap play.

Hyperbola Equation Given Graph | Grade 11 FunctionsKevinmathscience

Exponential Equation Given Graph | Grade 11 FunctionsKevinmathscience

Parabola How to Find the Equation Grade 10Miss Martins Maths and Science

Now try it on a real exam question

No sign-up. Takes 3 minutes.

Question 5.3 · November 2024 · Paper 1 · National (DBE) · 2 marks

Sketched below is the graph of

f (x) = \frac{a}{x + p} + q

having the domain

(- \infty; 1) \cup (1; \infty)

. The graph of

f

cuts the y-axis at

(0; 1)

. A line of symmetry of

f

is given by

g (x) = x - 3

5.3 Calculate the value of

a

.(2)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

More past paper questions: find the equation of a graph

Work each one out first, then open the memo and check every tick.

3. Question 4.2 · June 2025 · Paper 1 · Provincial · 3 marks
4.2 Determine the equation of the function $k (x) = \frac{a}{x} + q$ with the horizontal asymptote $y = 3$ . The straight line $f (x) = x + 2$ intersects with the graph of $k$ at the point $(2; 4)$ .(3)
Show the memo (3 ticks)Memo
1. ✓
  Identify the value of q $q = 3$
  1 mark · Find the equation of a graph
2. ✓
  Substitute the point to find 'a' $k (x) = \frac{a}{x} + 3$
  Substitute point $(2; 4)$ :
  $4 = \frac{a}{2} + 3$
  $1 = \frac{a}{2}$
  $a = 2$
  1 mark · Find the equation of a graph
3. ✓
  Write final equation $k (x) = \frac{2}{x} + 3$
  1 mark · Find the equation of a graph
4. Question 5.2 · November 2025 · Paper 1 · Provincial · 3 marks
The graphs of $f (x) = \frac{a}{x + p} + q$ and $g (x) = \frac{x}{3} + c$ are drawn below. C $(3; - 1)$ is the point of intersection between the asymptotes of $f$ . A and B are $x$ - and $y$ -intercepts of $f$ and $g$ respectively. E $(4; 2)$ is a point on $f$ in the first quadrant. $Diagram for this question$
5.2 Determine the equation of $f$ .(3)
Show the memo (3 ticks)Memo
1. ✓
  Equation with $p$ and $q$ $f (x) = \frac{a}{x - 3} - 1$
  1 mark · Find the equation of a graph
2. ✓
  Substitution of $(4; 2)$ $2 = \frac{a}{4 - 3} - 1$
  1 mark · Find the equation of a graph
3. ✓
  Equation of $f$ $a = 3$
  $f (x) = \frac{3}{x - 3} - 1$
  1 mark · Find the equation of a graph
5. Question 5.2 · November 2023 · Paper 1 · Provincial · 3 marks
The diagram below shows the graph of $f (x) = \frac{a}{x + p} + q$ . The asymptotes of $f$ intersect at $(- 3; - 1)$ and $f$ cuts the $x$ -axis at $x = - 5$ . $Diagram for this question$
5.2 Determine the value of $a$ .(3)
Show the memo (3 ticks)Memo
1. ✓
  Substituting for $p$ and $q$ $f (x) = \frac{a}{x + p} + q$
  $= \frac{a}{x + 3} - 1$
  1 mark · Find the equation of a graph
2. ✓
  Substituting for $x$ and $y$ $0 = \frac{a}{- 5 + 3} - 1$
  1 mark · Find the equation of a graph
3. ✓
  Answer $1 = \frac{a}{- 2}$
  $a = - 2$
  1 mark · Find the equation of a graph

Free on Android

Know exactly which skill is costing you marks.

Mark past papers tick by tick in the NavyBlue app. It remembers every mark you lose, shows you the skills to fix first, and picks your next questions.

The NavyBlue app showing a learner's weak skills