# Maths Paper 1, November 2024, question 6.4

> The diagram below shows the parabola f(x) = -x^2 + 6x + 7 and a straight line g. Marked mark by mark. Q6.4, Maths Paper 1 November 2024, 5 marks.

Canonical: https://sharpkop.co.za/maths/2024-nov-p1/q6-4/
Last updated: 2026-11-12

Subject: Maths. Source: Based on Nov 2024 · Paper 1 · Q6.4. Marks: 5. Not yet checked by a teacher.

## Question 6.4 (5 marks)

The diagram below shows the parabola $f(x) = -x^2 + 6x + 7$ and a straight line $g$. The line $g$ has gradient $2$ and passes through the point $(2;\,11)$, so $g(x) = 2x + 7$. The function $k$ is obtained by shifting $f$ horizontally, so that $k(x) = f(x+m) = -x^2 - 2mx - m^2 + 6x + 6m + 7$. Determine the value of $m$ for which $g$ is a tangent to $k$.

Figure: Graph of a parabola f that opens downwards and a straight line g that slopes upwards. Both cut the y-axis at (0; 7), and the line also passes through the point (2; 11). The line crosses the parabola a second time to the right of the y-axis.

## Practise it

[Answer this question](https://sharpkop.co.za/maths/2024-nov-p1/q6-4/) and see it marked mark by mark, with the reason for every lost mark.

## Related

- [More differential calculus questions](https://sharpkop.co.za/maths/differential-calculus/)
- [More functions and graphs questions](https://sharpkop.co.za/maths/functions-and-graphs/)
- [Maths Paper 1, November 2024](https://sharpkop.co.za/maths/2024-nov-p1/)
- [Grade 12 Maths past papers](https://sharpkop.co.za/maths/)

Questions are based on National Senior Certificate papers set by the Department of Basic Education. Sharpkop is not affiliated with or endorsed by the Department.