| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Solving quadratics and applications |
| Type | Completing the square, form and properties |
| Difficulty | Moderate -0.8 This question requires understanding that the minimum point gives the completed square form directly, then expanding to find axis intercepts. While it involves multiple steps, the techniques are straightforward applications of standard quadratic methods with no problem-solving insight required—easier than average for A-level. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02e Complete the square: quadratic polynomials and turning points1.02n Sketch curves: simple equations including polynomials |
| Answer | Marks |
|---|---|
| \(y=(x+3)^2-16\) | B1 B1 |
| Answer | Marks |
|---|---|
| When \(y=0\): \((x+3)^2=16 \Rightarrow x+3=\pm4 \Rightarrow x=1,\ -7\), so \((1,0)\) and \((-7,0)\) | B1 B1 |
| When \(x=0\): \(y=9-16=-7\), so \((0,-7)\) | B1 |
## Question 9:
**(i)**
$y=(x+3)^2-16$ | B1 B1 |
**(ii)**
When $y=0$: $(x+3)^2=16 \Rightarrow x+3=\pm4 \Rightarrow x=1,\ -7$, so $(1,0)$ and $(-7,0)$ | B1 B1 |
When $x=0$: $y=9-16=-7$, so $(0,-7)$ | B1 |
---9 The graph shows the function $y = x ^ { 2 } + b x + c$ where $b$ and $c$ are constants.\\
The point $\mathrm { M } ( - 3 , - 16 )$ on the graph is the minimum point of the graph.\\
\includegraphics[max width=\textwidth, alt={}, center]{3b6291ef-bef9-49de-a20f-591e621bed65-2_478_948_1871_588}\\
(i) Write down the function $y = \mathrm { f } ( x )$ in completed square form.\\
(ii) Hence find the coordinates of the points where the curve cuts the axes.
\hfill \mbox{\textit{OCR MEI C1 Q9 [5]}}