Cambridge IGCSE · Mathematics - Additional (0606)

Quadratic functions: Practice Questions

5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Quadratic functions.

10 questions26 marksFree, no account

Question 1

1 mark

Find the solution set of the inequality \(x^2 - 7x + 10 \le 0\).

Question 2

1 mark

Find the range of the function \(f(x) = x^2 - 4x + 7\) for the domain \(0 \le x \le 5\).

Question 3

1 mark

The line \(y = x + c\) is a tangent to the curve \(y = x^2 - 3x + 5\). Find the value of \(c\).

Question 4

1 mark

Find the coordinates of the turning point of the curve \(y = x^2 + 6x + 8\).

Question 5

1 mark

Find the range of values of \(k\) for which the equation \(x^2 + (k+1)x + 9 = 0\) has no real roots.

Question 6

2 marks

Write down the discriminant of the quadratic equation \( 2x^2 - 5x + 3 = 0 \) and state the nature of its roots.

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Question 7

4 marks

Find the coordinates of the points of intersection between the line \( y = 2x + 1 \) and the curve \( y = x^2 - 2 \).

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Question 8

6 marks

A curve has the equation \( y = kx^2 - 4x + (k-3) \), where \( k \) is a constant. Find the set of values of \( k \) for which the curve lies entirely below the \( x \)-axis.

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Question 9

4 marks

The quadratic function \( f(x) \) is defined by \( f(x) = 2x^2 - 12x + 19 \).
(a) Express \( f(x) \) in the form \( a(x-h)^2 + k \).
(b) State the coordinates of the minimum point of the graph of \( y = f(x) \).
(c) State the range of \( f(x) \) for all real values of \( x \).
(d) Sketch the graph of \( y = f(x) \), labelling the minimum point and the y-intercept.

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Question 10

5 marks

Find the range of values of the constant \(k\) for which the line \(y = 2x + k\) intersects the curve \(y = x^2 - 4x + 1\) at two distinct points.

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