1.1 Quadratic Equations

• form quadratic equations from real life situations
• solve quadratic equations by factorisation
• solve quadratic equations by completing the square
• solve quadratic equations using the quadratic formula
• use the discriminant to describe the nature of the roots
• solve quadratic equations graphically and read the roots from a graph
• apply quadratic equations in real life situations
• appreciate the use of quadratic equations in real life

“How are quadratic equations used in real life situations?”

“How does the shape of a quadratic graph help us to solve an equation?”

The titles are open to everyone. Reading a lesson needs an account — sign in or create one.

1. What a quadratic equation is
   40 min · 1 practice tasks · quiz
   Recognise a quadratic equation, write it in standard form and name its coefficients.
2. Forming equations from stories
   40 min · 1 practice tasks · quiz
   Turn a real scenario or statement into a quadratic equation in standard form.
3. Solving by factorisation
   40 min · 1 practice tasks · quiz
   Solve a quadratic equation by factorising and using the zero product rule.
4. More factorising patterns
   40 min · 1 practice tasks · quiz
   Factorise by a common factor, by the difference of two squares, and when a number leads.
5. Completing the square
   40 min · 1 practice tasks · quiz
   Solve a quadratic equation by writing it as a perfect square plus a number.
6. The turning point
   40 min · 1 practice tasks · quiz
   Use the completed square form to find the vertex and the greatest or least value.
7. The quadratic formula
   40 min · 1 practice tasks · quiz
   Solve any quadratic equation with the quadratic formula.
8. The discriminant
   40 min · 1 practice tasks · quiz
   Use b^2 - 4ac to describe the number and kind of roots.
9. Graphs of quadratic functions
   40 min · 1 practice tasks · quiz
   Draw a parabola and identify its roots, vertex, axis of symmetry and intercept.
10. Solving an equation from a graph
    40 min · 1 practice tasks · quiz
    Read the roots of a quadratic equation from the points where its graph meets the x-axis.
11. Application: area and dimensions
    40 min · 1 practice tasks · quiz
    Form and solve a quadratic equation from an area problem, rejecting the impossible root.
12. Application: speed, distance and time
    40 min · 1 practice tasks · quiz
    Solve a journey problem that leads to a quadratic equation in the speed.
13. Application: money and profit
    40 min · 1 practice tasks · quiz
    Use a quadratic profit model to find break-even points and the greatest profit.
14. Application: consecutive numbers
    40 min · 1 practice tasks · quiz
    Form and solve a quadratic from a number puzzle and consider both roots.
15. A line and a curve
    40 min · 1 practice tasks · quiz
    Solve a linear and a quadratic equation together and read the common points.
16. Quadratic equations: mixed review
    40 min · 1 practice tasks · quiz
    Bring together forming, factorising, completing the square, the formula and graphs.