CAIE A-Level Mathematics 1.1.1 Completing the square

Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise completing the square to rewrite quadratics, locate vertices, decide ranges and link a curve to a tangent horizontal line.

How this is tested

rewrite ax^2 + bx + c as a(x+b)^2+c and identify each constant correctly
use the completed-square form to find a vertex, range, or value of k for intersections

(a)

Express $4 x^{2}+10 x+6$ in the form $a(x+b)^{2}+c$ , where a, b and c are rational constants to be determined.

[ 2 ]

(b)

The curve with equation $y=4 x^{2}+10 x+6$ and the line y=k have exactly one point of intersection.

Using your answer to part (a) or otherwise, state the value of the constant k.

[ 1 ]

How this is tested

Question 3

Question 3(a)

Question 3(b)