Post on 31-Mar-2015
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Finding roots graphically
Finding roots by factorising
Finding roots using formula
Solving Quadratic Solving Quadratic w
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2 2x +7x +6
Q3. Solve (2x -1)(x -1) = 0
1. Factorise the following.
2. A TV is reduced by 20% to £200.
What was the original price.
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Int 2
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Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1.1. Use graphs to locate Use graphs to locate roots of a quadratic roots of a quadratic equation.equation.
1. To sow how to solve quadratic equations graphically.
2.2. Solve quadratic Solve quadratic equations by finding the equations by finding the roots.roots.
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Graphical Roots Graphical Roots
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Int 2Graphical Roots Graphical Roots
Finding the roots (solve) of a quadratic equation is simply finding where the graph crosses the x – axis ie. f(x) = 0
Example : Find the roots (solve) of the quadratic equations below.
3-2
f(x)
x 1-4
f(x)
x
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Int 2Graphical Roots Graphical Roots
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Int 2Graphical Roots Graphical Roots
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Int 2Graphical Roots Graphical Roots
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Now try MIA Ex 8Ch14 (page 228)
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Int 2Graphical Roots Graphical Roots
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(2,-2)
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Q. Write down the function represented by the graphs below given that they are of the form and a is either 1 or -1.
(1,4)
f(x)
x (0,-2)(-2,-4)
f(x)
x
y = a(x - b)2 + c
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Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1.1. To be able to factorise To be able to factorise quadratic equations.quadratic equations.
1. To explain how to find the roots (solve) quadratic equations by use of factorisation.
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Roots Roots
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When a number is multiplied by 0 the result is 0.
If 7b = 0 then b = 0
If ab = 0 then a = 0 or b = 0
If ( x-a )( x-b ) = 0 then either (x-a) = 0 or (x-b) = 0
Roots Roots
Note: The a,b in this form are NOT the a,b in the formf(x) ax2 + bx + c
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Factorise 2x2-x-1 = 0
( 2x+1)(x-1) = 0
2x+1 = 0
x-1 = 0
x = -0.5
x = 1
or
either
Factorise y2+ 3y = 0
y(y + 3) = 0
y = 0
y = -3
or
either
y + 3 = 0
Examples Factorise using FOIL or St. Andrew’s Cross
Roots Roots
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Find the roots of the quadratic equations.
Where it cut the x !!!!!!
Roots Roots
x2 + 7x + 10 = 0
x2 - 5x – 6 = 0 2x2 - 13x + 15 = 0
x2 + 6x + 8 = 0
x = 1.5, 5
x = -2, -5 x = -2, -4
x = 6, -1
(x – 6)(x + 1) = 0 (2x – 3)(x - 5) = 0
(x + 5)(x + 2) = 0 (x + 4)(x + 2) = 0
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Int 2
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Now try MIA Ex9 (page 229)
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Roots Roots
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2
2
y = -(x +4) + 1
3. Try and f actorise x -3x +3
1. Sketch.
2. A shop owner wants to makes a 15%
profit on a cd's he buys for £8.
How much does he need to sell them for ?
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Int 2
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Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1.1. To be able to solve To be able to solve quadratic equations quadratic equations using quadratic formula.using quadratic formula.
1. To explain how to find the roots (solve) quadratic equations by use quadratic formula.
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Int 2
Factorise Roots Factorise Roots
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When we cannot factorise or solve graphically quadratic equations we need to use the
quadratic formula.
Factorise Roots Factorise Roots
2-b ± (b -4ac)x =
2a
ax2 + bx + c
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Example : Solve x2 + 3x - 3
Factorise Roots Factorise Roots
2-(3) ± ((3) -4(1)(-3))x =
2(1)
ax2 + bx + c
1 3 -3
-3 ± 21=
2
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Factorise Roots Factorise Roots
-3 + 21x =
2-3 - 21
x = 2
and
x = 0.8 x = -3.8
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Use quadratic formula to solve the following :
Factorise Roots Factorise Roots
2x2 + 4x + 1 = 0
5x2 - 9x + 3 = 0 3x2 - 3x – 5 = 0
x2 + 3x – 2 = 0
x = 1.9, -0.9
x = -1.7, -0.3 x = -3.6, 0.6
x = 1.4, 0.4
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Now try MIA Ex10 (page 232)
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Factorise Roots Factorise Roots