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Learn: Quadratic Equations
AQA 7357 A Level Mathematics
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Welcome!Today we’ll explore quadratic equations, a key topic in AQA A Level Mathematics. Quadratics appear often in maths and science, so understanding them is essential!
What is a Quadratic Equation?A quadratic equation is any equation in the form ax² + bx + c = 0, where a, b, and c are constants, and a ≠ 0. They are used to describe curved graphs called parabolas.
Solving Quadratic EquationsThere are three main methods to solve quadratics: factorising, using the quadratic formula, and completing the square. Each method has its own advantages depending on the equation.
Quick check: Which of the following is a quadratic equation?
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Method 1: FactorisingTo solve a quadratic by factorising, find two numbers that multiply to c and add to b. Rewrite the equation, factorise, and solve for x.
To factorise x² + 5x + 6, find two numbers that multiply to {{blank0}} and add to {{blank1}}.
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Method 2: Quadratic FormulaThe quadratic formula is x = (-b ± √(b² - 4ac)) / 2a. It works for any quadratic equation and is especially useful when factorisation is difficult or impossible.
Quick check: What does the discriminant (b² - 4ac) tell us?
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Method 3: Completing the SquareCompleting the square involves rewriting a quadratic equation in the form (x + p)² = q. This makes it easier to solve by taking square roots.
Match the items on the left with their correct pairs on the right
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Review Time!Fantastic work so far! You've learned about quadratic equations and three methods to solve them: factorising, using the quadratic formula, and completing the square. Let's test your understanding!
Which of the following are true? (Select all that apply)
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Match the items on the left with their correct pairs on the right
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The graph of a quadratic is a {{blank0}}, and the turning point can be found by completing the {{blank1}}.
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Which of these is NOT a method to solve quadratic equations?
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Well done!You've successfully learned how to solve quadratic equations using factorising, the quadratic formula, and completing the square. Keep practising to become confident in using these methods!
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