Grade 10 Maths · Functions

Find the x-intercepts

Find where a graph cuts the x-axis by putting y = 0 and solving (for example y = x² − 4 cuts at (−2; 0) and (2; 0)).

past paper questions use it: 29 past paper questions use it
videos: 3 videos

Learn it: find the x-intercepts

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

Grade 9 Mathematics - Calculating the x and y intercepts of a straight lineMrs Townsend Mathematics - South Africa

Draw Parabola Grade 11 | Part 1 | Grade 11 FunctionsKevinmathscience

How To Find The X and Y Intercepts of a LineThe Organic Chemistry Tutor

Now try it on a real exam question

No sign-up. Takes 3 minutes.

Question 3.1 · May/June 2025 · Paper 2 · National (DBE) · 2 marks

In the diagram below,

Δ SRT

is drawn where R lies on the x-axis and S lies to the left of R. T lies on the y-axis and the coordinates of S are

(m; 1)

.

The equation of RT is

2 x - y + 10 = 0

3.1 Calculate the coordinates of R.(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 x-intercepts

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

3. Question 6.2 · May/June 2024 · Paper 1 · National (DBE) · 3 marks
The graphs of $f (x) = x^{2} - 2 x - 3$ and $g (x) = m x + c$ are drawn below. D and E are the $x$ -intercepts and P is the $y$ -intercept of $f$ . The turning point of $f$ is T $(1; - 4)$ . The graphs of $f$ and $g$ intersect at P and E.
6.2 Calculate the coordinates of D and E.(3)
Show the memo (3 ticks)Memo
1. ✓
  Equate equation to zero $x^{2} - 2 x - 3 = 0$
  1 mark · Find the x-intercepts
2. ✓
  Both x-values $(x - 3) (x + 1) = 0$
  $x = 3$ or $x = - 1$
  1 mark · Solve a quadratic by factorising
3. ✓
  Final coordinates $D (- 1; 0), E (3; 0)$
  1 mark · Find the x-intercepts
4. Question 4.4 · May/June 2025 · Paper 1 · National (DBE) · 4 marks
The graph of $f (x) = \frac{4}{x - 3} + 4$ is drawn below. M is the point where the asymptotes of $f$ intersect. C and D are the x- and y-intercepts respectively of $f$ . A is the point on $f$ that is closest to M.
4.4 Determine the values of $x$ for which $f (x) \leq 0$ .(4)
Show the memo (2 ticks)Memo
1. ✓
  Find the x-intercept C by equating f(x) to 0 $\frac{4}{x - 3} + 4 = 0$
  $\frac{4}{x - 3} = - 4$
  $4 = - 4 (x - 3)$
  $- 1 = x - 3$
  $x = 2$
  $C (2; 0)$
  2 marks · Find the x-intercepts
2. ✓
  Determine interval from the graphFrom the graph, $f (x) \leq 0$ occurs between the x-intercept and the vertical asymptote.
  $2 \leq x < 3$
  2 marks · Solve an inequality from a graph
5. Question 7.4.2 · May/June 2025 · Paper 2 · National (DBE) · 3 marks
In the diagram, the graphs of $f (x) = 2 cos x + 1$ and $g (x) = sin 2 x$ are drawn for the interval $x \in [- 18 0^{\circ}; 18 0^{\circ}]$ .
7.4 Use the graphs to determine the values of x, in the interval $x \in [- 18 0^{\circ}; 18 0^{\circ}]$ for which:
7.4.2 $cos x \leq - \frac{1}{2}$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Relate the inequality to the given graph f(x) $cos x \leq - \frac{1}{2}$
  Multiply by 2:
  $2 cos x \leq - 1$
  Add 1 to both sides:
  $2 cos x + 1 \leq 0$
  This means we are looking for where $f (x) \leq 0$ .
  1 mark · Solve an inequality from a graph
2. ✓
  Find the x-intercepts of f(x) $2 cos x + 1 = 0$
  $cos x = - \frac{1}{2}$
  Reference angle $= 6 0^{\circ}$
  $x = 18 0^{\circ} - 6 0^{\circ} = 12 0^{\circ}$
  $x = - 18 0^{\circ} + 6 0^{\circ} = - 12 0^{\circ}$
  1 mark · Find the x-intercepts
3. ✓
  Determine the intervals where the graph is below or on the x-axis $x \in [- 18 0^{\circ}; - 12 0^{\circ}] \cup [12 0^{\circ}; 18 0^{\circ}]$
  
  OR
  
  $- 18 0^{\circ} \leq x \leq - 12 0^{\circ}$ or $12 0^{\circ} \leq x \leq 18 0^{\circ}$
  1 mark · Solve an inequality from a graph
6. Question 3.2.1 · March 2025 · Provincial · 2 marks
3.2 Sketched below is the parabola $f$ and the straight line $g (x) = 3 x + 6$ . R and S are the x-intercepts of $f$ , and $P (- \frac{1}{2}; 9)$ is its turning point. $g$ has its x-intercept at R.
3.2.1 Calculate the coordinates of R.(2)
Show the memo (2 ticks)Memo
1. ✓
  Solve for x-intercept of g $3 x + 6 = 0$
  $3 x = - 6 \to x = - 2$
  1 mark · Find the x-intercepts
2. ✓
  State coordinates $R (- 2; 0)$
  1 mark · Find the x-intercepts

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