# Quadratics ax2 + bx + c.

## Presentation on theme: "Quadratics ax2 + bx + c."— Presentation transcript:

Quadratics ax2 + bx + c

Multiplying brackets (FOIL)
x2 +2x +3x +6 x2 +5x +6 Outside ( x+ 3)(x + 2) Inside Last First

Multiplying brackets (FOIL) (with minus numbers)
x2 -2x +4x -8 x2 +2x -8 Outside ( x+ 4)(x - 2) Inside Last First

Multiplying brackets (FOIL) (with minus numbers)
x2 -4x -3x +12 x2 -7x +12 Outside ( x-3)(x - 4) Inside Last First

y y = x2 +3x -4 When y =0 X = 1 or -4 x

You can find a quadratic from it’s roots

Quadratics For example, x = 3 or -2 When y =0 (x - 3) =0 or (x + 2 ) =0 Multiply the brackets x2 - x - 6 = 0

The x’s have to multiply to make the first term x2 +5x +6 ( x )(x ) +3 +2 The numbers have to add up to +5 and multiply to make +6

Check it out Outside ( x+ 3)(x + 2) Last Inside First
x2 +2x + 3x = (x2 + 5x +6)

The x’s have to multiply to make the first term 2x2 - 4x - 6 2x x -3 = -6x -6x +2x = -4x ( 2x )(x ) +2 - 3 The numbers have to add up to -4 and multiply to make -6

Examples to remember (a – b)(a + b) a2 +ab –ab – b2 = a2 – b2

The same applies to all these type of equations
Examples to remember The same applies to all these type of equations a2 – 9 = (a-3)(a+3)

The same applies to all these type of equations
Examples to remember The same applies to all these type of equations 4a2 – 36 = (2a -6)(2a+6)

ax2 +bx +c is the standard form of a quadratic equation (where a, b and c represent numbers) to find x use the equation x = (-b ± √(b2 – 4ac))/2a