1.1 Quadratic Expressions and Equations

• Perfect squares in quadratic expressions; completing the square
• Deriving the quadratic formula; the discriminant; solving quadratic equations with the formula
• Simultaneous equations, one linear and one quadratic, by substitution
• Forming quadratic equations from roots and from real-life situations

• identify perfect squares in quadratic expressions and equations
• solve quadratic equations by completing the square
• derive the quadratic formula using completing the square
• solve quadratic equations using the quadratic formula
• solve simultaneous equations involving linear and quadratic equations
• apply quadratic equations in real-life situations
• appreciate the application of quadratic equations in real-life situations

“How are quadratic equations applied in day to day life?”

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1. Perfect-square quadratics
   40 min · 1 practice tasks · quiz
   Decide whether a quadratic is the square of a linear expression, using factorisation and the test b squared equals 4ac.
2. Completing the square
   40 min · 1 practice tasks · quiz
   Rewrite a quadratic as a perfect square plus or minus a number, first when the x^2 coefficient is 1 and then when it is not.
3. Roots by completing the square
   40 min · 1 practice tasks · quiz
   Solve monic quadratic equations by completing the square, including a repeated root and a root that needs a square root.
4. Completing the square when a is not 1
   40 min · 1 practice tasks · quiz
   Divide a quadratic equation by its leading coefficient, then complete the square and keep every root.
5. Deriving the quadratic formula
   40 min · 1 practice tasks · quiz
   Complete the square on ax^2 + bx + c = 0 and arrive at x = [-b plus or minus the square root of (b^2 - 4ac)] divided by 2a.
6. The discriminant
   40 min · 1 practice tasks · quiz
   Use b^2 - 4ac to decide whether a quadratic equation has two distinct real roots, one repeated real root, or no real root.
7. Using the quadratic formula
   40 min · 1 practice tasks · quiz
   Solve quadratic equations with the formula, simplify surd roots, and stop when the discriminant is negative.
8. A line and a quadratic together
   40 min · 1 practice tasks · quiz
   Solve a linear equation and a quadratic equation simultaneously by substitution, and read zero, one or two meeting points from the discriminant.
9. Building a quadratic
   40 min · 1 practice tasks · quiz
   Form x^2 - (sum)x + product = 0 from two roots, and form a quadratic from a rectangular area, rejecting a negative length.
10. Quadratics in a story
    40 min · 1 practice tasks · quiz
    Solve a product of consecutive numbers, read a greatest height from a completed square, and find two numbers from their sum and the sum of their squares.