# Starter. Use the formula to solve What makes the difference?

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Starter

Use the formula to solve

What makes the difference?

The Discriminant

3 possible outcomes 2 roots 2 ‘zeros’ 2 x-intercepts 1 root, ‘zero’, x-intercept No real roots, ‘zeros’ or x-intercepts

Time for notes

Cut out the square and fold each corner to the centre like this

Write on each of the flaps Glue the shape into your notes

Under the first flap -------------

Under the second flap

Under the 3rd flap -------------

Under the final flap -------------

Homework On Moodle – look for the Quadratics topic To be completed on file paper – NOT IN YOUR INDEPENDENT STUDY BOOKS To be named, dated and set out properly Questions and answers Marked in a second colour Comments in a third colour HAND IN DATE – MONDAY 6 th OCTOBER

Task – match up 2 sheets – one all numbers other algebra Note: If the value of b 2 —4ac is a positive square number then you should be able to factorise the quadratic If the value of b 2 - 4ac is positive but not square then just use the formula and leave surds in your answer to find the roots

Factorises (with integers)Does not factorise Has one real root (2 identical roots) Graph just touches the x-axis If the quadratic equation has one root then it always factorises Has two real and different roots Graph crosses the x-axis Has no real roots Graph does not touch or cross the x-axis If the quadratic equation has no real roots then it never factorises

Factorises (with integers)Does not factorise Has one real root (2 identical roots) Graph just touches the x-axis If the quadratic equation has one root then it always factorises Has two real and different roots Graph crosses the x-axis Has no real roots Graph does not touch or cross the x-axis If the quadratic equation has no real roots then it never factorises

Factorises (with integers)Does not factorise Has one real root (2 identical roots) Graph just touches the x-axis If the quadratic equation has one root then it always factorises Has two real and different roots Graph crosses the x-axis Has no real roots Graph does not touch or cross the x-axis If the quadratic equation has no real roots then it never factorises

Factorises (with integers)Does not factorise Has one real root (2 identical roots) Graph just touches the x-axis If the quadratic equation has one root then it always factorises Has two real and different roots Graph crosses the x-axis Has no real roots Graph does not touch or cross the x-axis If the quadratic equation has no real roots then it never factorises

Factorises (with integers)Does not factorise Has one real root (2 identical roots) Graph just touches the x-axis If the quadratic equation has one root then it always factorises Has two real and different roots Graph crosses the x-axis Has no real roots Graph does not touch or cross the x-axis If the quadratic equation has no real roots then it never factorises Can you factorise them?

Extension Find the possible values of the constant given that the equation has a repeated root. For a repeated root,

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