Algebra IV (AQA GCSE Further Maths): Quizzes

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Quadratic equations
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What is the standard form of a quadratic equation?

ax2+bx+c=0ax^2 + bx + c = 0

In standard form ax2+bx+c=0ax^2 + bx + c = 0, which restriction must apply?

a≠0a \neq 0

How many main methods exist for solving quadratic equations?

Three

What does the zero product property state?

If a product equals zero, at least one factor must be zero

Before factorising, what arrangement is required?

All terms on one side, zero on the other

When completing the square, what do you do with the coefficient of xx?

Halve it, then square it

If coefficient of x2x^2 is not 1, what must you do before completing the square?

Divide entire equation by coefficient

What is the quadratic formula?

x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

If discriminant b2−4ac>0b^2 - 4ac > 0, how many real solutions exist?

Two different real solutions

What does it mean when the discriminant b2−4ac=0b^2 - 4ac = 0?

One repeated real solution

What shape is the graph of a quadratic function?

A parabola (U-shaped curve)

What do the solutions to ax2+bx+c=0ax^2 + bx + c = 0 represent on a graph?

The x-intercepts of the parabola

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