Cambridge Assessment International Education · Cambridge O Level

4037 Additional Mathematics

Paper 1 · Variant 1

May/June 2023 · Component 11

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Questions

Question

10 marks

(a)

Rewrite the expression

5 x^{2} - 14 x + 8

in the completed-square form

a (x + b)^{2} + c

, determining the values of the constants

a

b

and

c

(b)

Using your completed-square result from part (a), state the coordinates of the stationary point of the curve

y = 5 x^{2} - 14 x + 8

(c)

Sketch the graph of

y = 5 x^{2} - 14 x + 8

, and give the coordinates of each point at which your graph crosses the coordinate axes.

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(d)

Determine the range of values of the constant

k

for which the equation

5 x^{2} - 14 x + 8 = k

has exactly four distinct real roots.

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