Grade 11 Maths · Functions

Find k for number of roots

Use the turning points of a graph to find the values of k for which a line y = k cuts it a given number of times.

past paper questions use it: 5 past paper questions use it
videos: 4 videos

Learn it: find k for number of roots

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

For Which Values of K | Grade 11 FunctionsKevinmathscience

Cubic Function Translations with k (mathdou) Grade 12 +Dou Kleefstra

translations on Cubic graphs, for which values of k will the equation f(x) = k have 3 distinct rootsBenit mathematics

Now try it on a real exam question

No sign-up. Takes 3 minutes.

Question 5.2 · May/June 2025 · Paper 1 · National (DBE) · 2 marks

The graph of

f (x) = a (x + p)^{2} + q

is drawn below.

C (- 1; 4)

is the turning point of

f

B (- 3; - 4)

is a point on

f

5.2 Determine the values of

k

for which

h (x) = f (x) + k

will have no real roots.(2)

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

More past paper questions: find k for number of roots

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

3. Question 9.4 · November 2024 · Paper 1 · National (DBE) · 2 marks
$A (1; 9)$ and $B (\frac{5}{2}; 8)$ are the turning points of graph $f$ below. $C (0; 7)$ is the y-intercept of $f$ .
9.4 Determine the value of $k$ for which $y = f (x) + k$ will have THREE positive x-intercepts.(2)
Show the memo (1 tick)Memo
1. ✓
  Determine vertical shift rangeMin turning point is 8. Max turning point is 9.
  To have 3 roots, shift down between 8 and 9 units.
  $- 9 < k < - 8$
  2 marks · Find k for number of roots
4. Question 6.4.1 · November 2025 · Paper 1 · Provincial · 2 marks
The graphs of $f (x) = - x^{2} - 6 x$ and $g (x) = a x^{2} + b x$ are drawn below. $g$ is the reflection of $f$ along the $x$ -axis. A and B $(- 5; n)$ are symmetrical on $f$ along $x = - p$ , i.e. the axes of symmetry. $Diagram for this question$
6.4 Determine the value(s) of $k$ for which:
6.4.1 $f (x) = - x^{2} - 6 x + k$ will have non-real roots.(2)
Show the memo (1 tick)Memo
1. ✓
  Answer $k < - 9$
  2 marks · Find k for number of roots
5. Question 6.6 · November 2024 · Paper 1 · Provincial · 3 marks
Sketched below is the graph of $f (x) = x^{2} - 4 x - 5$ for $x \in (- \infty; 6]$ .

A and B are the $x$ -intercepts and C the $y$ -intercept of $f$ . $Diagram for this question$
6.6 For which values of $k$ will $f (x) - k = 0$ have just one real root?(3)
Show the memo (2 ticks)Memo
1. ✓
  $f (2) = - 9$ $f (x) = k$
  $x = \frac{- b}{2 a} = - \frac{- 4}{2 ( 1 )} = 2$
  $f (2) = - 9$
  1 mark · Find turning point of a parabola
2. ✓
  $k = - 9$ or $k > 7$ $k = - 9$ or $k > 7$ $Memo diagram$
  2 marks · Find k for number of roots

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