1. Starter To make sure that you can re-arrange equations
Make “x” the subject of the formula
v = ω√(a² -x²)
so x= ?
5 November, 2019
INTO - Foundation L4/5 MH

2. Lesson 4-5 Quadratic equations
Objectives
- To solve quadratic equations by factorisation
- To solve quatratic equations by completing the square
- To solve quadratic equations by formula
5 November, 2019
INTO - Foundation L4/5 MH

3. Quadratic equations These occur naturally e.g.
The length of a rectangular field is 40m greater than its width. Its area is 6000m2
Form an equation to find the length of the field
5 November, 2019
INTO - Foundation L4/5 MH

4. Quadratic equations Usually have two solutions Look like parabolas
Take the form
Do you know how a,b,c effect the quadratic curve ?
5 November, 2019
INTO - Foundation L4/5 MH

5. They look something like this
5 November, 2019
INTO - Foundation L4/5 MH

6. Factorising quadratics
Factorise
X2+7x ( x ) ( x )
X2-2x ( x ) (x )
12X2-17x factors of 12 (4,3), (6,2),(12,1)
factors of 7 (7,1)
( x ) ( x )
5 November, 2019
INTO - Foundation L4/5 MH

7. Solving quadratics
Once we have factorised the quadratic we have the solution
X2+5x+6 = (x+2)(x+3)=0 so x=-2 and x=-3
These are also known as the roots of the equation
Obviously, not all quadratics factorise !!
5 November, 2019
INTO - Foundation L4/5 MH

8. Can’t factorise it Then we complete the square OR
We use the quadratic formula
Completing the square implies that the form of
Is written as
5 November, 2019
INTO - Foundation L4/5 MH

9. Complete the square and solve
8x2 + 64x – 40 Step 1 divide by a Step 2 write Step 3 subtract the squared term
5 November, 2019
INTO - Foundation L4/5 MH

10. To solve Rearrange the equation Take the square roots of both sides
Rearrange for x
5 November, 2019
INTO - Foundation L4/5 MH

11. Derive the Quadratic formula
5 November, 2019
INTO - Foundation L4/5 MH

12. Derive quadratic formula
5 November, 2019
INTO - Foundation L4/5 MH

13. Worksheet I have a worksheet to hand out
Factorise the first sets of equations
Complete the square to solve the second set of equations
Use the quadratic formula to solve the last set of equations
5 November, 2019
INTO - Foundation L4/5 MH