Upload
beverly-walsh
View
228
Download
0
Tags:
Embed Size (px)
Citation preview
Quadratics
Solving Quadratic Equations
Solving by Factorising
equations. elementary theSolve :3 Step
.0or 0either
then,0 if :lawfactor null the Use:3 Step
side.other thefactoriseFully :2 Step
side. one to termsall ingby tranfer
zero toequalequation theof side one make :1 Step
rue.equation t themake which of valuesare
0cbx of solutionsor Roots:Definition 2
ba
ba
x
ax
Example 1
72
3 (e)
10116 (d)
414 (c)
65 (b)
053 (a)
:for x following theSolve
2
2
2
2
xx
xx
xx
xx
xx
Solving by Completing the Square
for x. valuesthe
find andequation theundo toable then are We
square. the
completing of method theusingby
form in the 0 writeWe2
2
qpxa
cbxax
Example 2
073 (c)
75 (b)
3232 (a)
:for x Solve
2
2
2
x
x
x
Example 3
03102 (c)
043 (b)
014 (a)
:square thecompletingby following theSolve
2
2
2
xx
xx
xx
Solving using the Quadratic Formula
a
acbbx
cbxax
2
4
:is 0 osolution t The
2
2
Proof
Example 4
133-x
5x (d)
0432 (c)
022 (b)
0103 (a)
:formula quadratic theusing following theSolve
2
2
2
x
xx
xx
xx
Approximate solution using Technology
• Draw the graph using the graphic calculator In y=
• Use an appropriate window• Find where the graph cuts the x-axis using 2nd
calc buttons
Example 5
1221x (c)
0143x (b)
0115 (a)
:osolution t eapproximat thefind y to technologUse
2
2
xx
x
xx
Complex Roots
• Use the quadratic formula to solve• If the number under the square root is
negative treat it as an imaginary number and continu with the solution.
Example 6
0134 (c)
0254x (b)
09 (a)
:for x Solve
2
2
2
xx
x
This Weeks Work
• Page 26 Ex 1E1 Q1 – 3• Page 28 Ex1E2 Q1 – 3• Page 31 Ex 1E3 Q1, 2• Page 12 Ex 1E4 Q1, 2• Page 33 Ex 1E5 Q1, 2