Quadratic Functions: worked exam questions
12 solved quadratic functions questions, each worked line by line the way the 0606 mark scheme rewards. Learn the method in the Quadratic Functions topic notes, then see it applied here.
A Quadratic in Disguise with a Square Root
Solve x − 5√x + 6 = 0 by substituting u = √x to reveal a quadratic, then squaring back, a 0606 question on quadratic-type equations.
Completing the Square for a Maximum
Write 3 + 4x − 2x² in completed-square form and read off its maximum, a 0606 question on completing the square when the x² coefficient is negative.
Completing the Square to Find the Minimum
Write 2x² − 12x + 5 in the form a(x + b)² + c, then read off the minimum point directly, a 0606 Paper 1 question where the completed square does all the work.
Intersection of a Line and a Quadratic Curve
Find where a line crosses a quadratic curve by solving simultaneously, a 0606 question producing a quadratic with two intersection points.
Maximum Area with Completing the Square
Maximise the area of a rectangular pen against a wall using completing the square, a 0606 quadratic optimisation done without calculus.
No Real Roots: Finding a Range of k
Find the values of k for which a quadratic has no real roots using b² − 4ac < 0, a 0606 discriminant question giving a bounded range.
Range of a Quadratic on a Restricted Domain
Find the range of x² − 4x + 7 over all reals and over 0 ≤ x ≤ 3, a 0606 question where the vertex and the endpoints together decide the answer.
Sketching a Parabola: Intercepts and Vertex
Find the intercepts and vertex of a quadratic to sketch it, a 0606 question pulling together factorising and completing the square for the key features.
Solving a Quadratic Inequality
Solve 2x² − 5x − 3 > 0 by factorising and reading the parabola, the 0606 method that beats sign tables and gets the 'inside or outside' choice right.
Two Distinct Roots: Finding a Range of k
Find the values of k for which a quadratic has two distinct real roots, a 0606 discriminant question that ends in an inequality, not an equation.
Using the Discriminant for Equal Roots
Find the values of k for which a quadratic has two equal roots by setting b² − 4ac = 0, a 0606 discriminant question that reduces to a quadratic in k.
When Is a Line a Tangent to a Curve?
Find k so that a line is a tangent to a quadratic curve, using the discriminant of the combined equation, a 0606 favourite linking lines, curves and roots.
Worked examples show the routine. A tutor builds it into your child.
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