Theory of Intelligence
A-LEVEL•Mathematics•Quadratics•Exercise 1.1 · Quadratics

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12 original exam-style questions on quadratics, with worked solutions and mark guides.

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Question 1

🟢 Foundation · [3 marks]

Express 2x2−12x+232x^2 - 12x + 23 in the form a(x+b)2+ca(x+b)^2 + c, and state the coordinates of the vertex of y=2x2−12x+23y = 2x^2 - 12x + 23.

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Step-by-Step Solution

Question 1

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Solution

2x2−12x+23=2[x2−6x]+23=2[(x−3)2−9]+23=2(x−3)2−18+23=2(x−3)2+5\begin{aligned} 2x^2 - 12x + 23 &= 2\left[x^2 - 6x\right] + 23 \\ &= 2\left[(x-3)^2 - 9\right] + 23 \\ &= 2(x-3)^2 - 18 + 23 \\ &= 2(x-3)^2 + 5 \end{aligned}

So a=2a = 2, b=−3b = -3, c=5c = 5, and the vertex is (3, 5)(3,\ 5), which is a minimum point.

Mark guide

MarkAwarded for
B1a=2a = 2 and b=−3b = -3
B1c=5c = 5
B1Vertex (3, 5)(3,\ 5)
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