quadratics ax 2 + bx + c. multiplying brackets (foil) x 2 +5x +6 outside ( x+ 3)(x + 2) first x2x2...
TRANSCRIPT
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QUADRATICS
ax2 +
bx
+ c
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MULTIPLYING BRACKETS (FOIL)
x2 +5x +6
Outside
( x+ 3)(x + 2)
First
x2
InsideLast
+2x
+3x
+6
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MULTIPLYING BRACKETS (FOIL) (WITH MINUS NUMBERS)
x2 +2x -8
Outside
( x+ 4)(x - 2)
First
x2
InsideLast
-2x
+4x
-8
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MULTIPLYING BRACKETS (FOIL) (WITH MINUS NUMBERS)
x2 -7x +12
Outside
( x-3)(x - 4)
First
x2
InsideLast
-4x
-3x+12
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y
xy = x2 +3x -4
When y =0
X = 1 or -4
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QUADRATICS
You can find a
quadratic from it’s
roots
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QUADRATICS
For example, x = 3 or -2
When y =0 (x - 3) =0
or (x + 2 ) =0Multiply the
bracketsx2 - x - 6 = 0
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FACTORISING AND SOLVING QUADRATICS
x2 +5x +6
( x )(x )
The numbers have to add up to +5 and multiply to make +6
+3
+2
The x’s have to multiply to make the first term
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CHECK IT OUT
Outside
( x+ 3)(x + 2)
First
Inside
Last
x2 +2x + 3x + 6 = (x2 + 5x +6)
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FACTORISING AND SOLVING QUADRATICS
2x2 - 4x - 6
( 2x )(x )
The numbers have to add up to -4 and multiply to make -6
+2
- 3
The x’s have to multiply to make the first term
2x x -3 = -6x
-6x +2x = -4x
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EXAMPLES TO REMEMBER
(a – b)(a + b)
a2 +ab –ab – b2
= a2 – b2
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EXAMPLES TO REMEMBER
The same applies to all these type
of equations
a2 – 9
= (a-3)(a+3)
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EXAMPLES TO REMEMBER
The same applies to all these type
of equations
4a2 – 36
= (2a -6)(2a+6)
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SOLVING USING THE QUADRATIC FORMULA
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
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2x2 +8x + 6 = 0a = 2, b = 8 , c = 6
x = (-8 ± √(82 – 4*2*6))/2*2=(-8 ± √(64 – 48))/4
= ( -8 ± √16)/4(-8 ± 4)/4
= -12/4 or -4/4= -3 or -1
SOLVING USING THE QUADRATIC FORMULA
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SOLVING USING THE QUADRATIC FORMULA
x2 -10x + 34 = 0x = (10 ± √(102 – 4*1*-34))/2
=(10 ± √(100 – 136))/2= ( 10 ± √-36)/2
(10 ± 6i)/2= 5 + 3i or 5 – 3i
i is an imaginary number (i2 = -1)
Cannot havea zero square number so has to be multipliedby i2 to make it positive