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Mathematics · 2026 · 4 marks
CBSE 2026 · Region 3 · Set 1 · Q36
During a theatre drama, a backdrop of building arches was used. The shape of the curve shown below can be represented by the polynomial $\displaystyle \mathrm{p}(\mathrm{x})=-\mathrm{x}^{2}+2 \mathrm{x}+8$, where x is the length (in feet) on stage level.
Based on the figure given above, answer the following questions :(i)Determine the height of the arch.(ii)Find zeroes of the polynomial p(x). Which points on the graph represent the zeroes ?Find the span of the arch on the stage floor.(iii)Write the coordinates of the point of intersection of the above curve with the y -axis.
During a theatre drama, a backdrop of building arches was used. The shape of the curve shown below can be represented by the polynomial $\displaystyle \mathrm{p}(\mathrm{x})=-\mathrm{x}^{2}+2 \mathrm{x}+8$, where x is the length (in feet) on stage level.
Based on the figure given above, answer the following questions :
(i)
Determine the height of the arch.
(ii)
Find zeroes of the polynomial p(x). Which points on the graph represent the zeroes ?
Find the span of the arch on the stage floor.
(iii)
Write the coordinates of the point of intersection of the above curve with the y -axis.
Marking-scheme solution
(i)
$\displaystyle p(1)=-(1)^{2}+2 \times 1+8=9$
So, height of the arch is $\displaystyle 9$ feet.
(ii)
\[\begin{array}{l}
\mathrm{p}(\mathrm{x})=-\mathrm{x}^{2}+2 \mathrm{x}+8 \\
\quad=-(\mathrm{x}-4)(\mathrm{x}+2) \\
\text { zeroes are }-2 \text { and } 4
\end{array}
\]
Points B and A on the graph represent the zeroes.
\[\begin{aligned}
p(x) & =-x^{2}+2 x+8 \\
& =-(x-4)(x+2)
\end{aligned}
\]
∴ zeroes are -$\displaystyle 2$ and 4.
Hence, Coordinates of point A and B are $\displaystyle (4,0)$ and $\displaystyle (-2, 0)$ respectively.
Span of the arch on the stage floor, $\displaystyle \mathrm{AB}=4+2=6$
So, span of the arch on the stage floor is $\displaystyle 6$ feet.
(iii)
$\displaystyle \mathrm{p}(0)=-(0)^{2}+2 \times 0+8=8$
∴ the given curve intersects y-axis at $\displaystyle (0,8)$
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CBSE Class 10 Mathematics past-paper question from the 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.