Easy -1.8 This is a straightforward reading-from-graph question requiring only visual interpretation of where a parabola is above the x-axis. No algebraic manipulation or problem-solving is needed—students simply identify that y > 0 between the roots, making it significantly easier than average A-level questions.
1 The graph of \(y = a x ^ { 2 } + b x + c\) has roots \(x = 2\) and \(x = 5\), as shown in the diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{de8a7d38-a665-4feb-854e-ac83f413d133-02_905_963_717_625}
State the set of values of \(x\) which satisfy
$$a x ^ { 2 } + b x + c > 0$$
Tick ( \(\checkmark\) ) one box.
$$\begin{aligned}
& \{ x : x < 2 \} \cup \{ x : x > 5 \} \\
& \{ x : 0 < x < 2 \} \cap \{ x : x > 5 \} \\
& \{ x : 2 < x < 5 \} \\
& \{ x : 2 > x > 5 \}
\end{aligned}$$
\includegraphics[max width=\textwidth, alt={}, center]{de8a7d38-a665-4feb-854e-ac83f413d133-02_118_115_1950_1087}
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1 The graph of $y = a x ^ { 2 } + b x + c$ has roots $x = 2$ and $x = 5$, as shown in the diagram below.\\
\includegraphics[max width=\textwidth, alt={}, center]{de8a7d38-a665-4feb-854e-ac83f413d133-02_905_963_717_625}
State the set of values of $x$ which satisfy
$$a x ^ { 2 } + b x + c > 0$$
Tick ( $\checkmark$ ) one box.
$$\begin{aligned}
& \{ x : x < 2 \} \cup \{ x : x > 5 \} \\
& \{ x : 0 < x < 2 \} \cap \{ x : x > 5 \} \\
& \{ x : 2 < x < 5 \} \\
& \{ x : 2 > x > 5 \}
\end{aligned}$$
\includegraphics[max width=\textwidth, alt={}, center]{de8a7d38-a665-4feb-854e-ac83f413d133-02_118_115_1950_1087}\\
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\hfill \mbox{\textit{AQA Paper 2 2023 Q1 [1]}}