Cambridge International Mathematics

QUADRATIC EQUATIONS WITH NO REAL SOLUTIONS Consider x^2 +2x+5=0. Using the quadratic formula, the solutions are: x= ¡ 2 § p 4 ¡4 ...

Example 8 Self Tutor If y=2x^2 +4x¡ 5 find the value ofywhen: a x=0 b x=3. a When x=0, y= 2(0)^2 + 4(0)¡ 5 =0+0¡ 5 =¡ 5 b When x ...

5 Find the value(s) ofxfor which: a f(x)=3x^2 ¡ 3 x+6takes the value 6 b f(x)=x^2 ¡ 2 x¡ 7 takes the value ¡ 4 c f(x)=¡ 2 x^2 ¡ ...

2 2 4 8 12 4 x y O Example 10 Self Tutor Draw the graph of y=x^2 +2x¡ 3 from a table of values fromx=¡ 3 tox=3. Consider f(x ...

Part 2: Graphs of the form y=(x¡h)^2 What to do: 1 Using agraphing packageorgraphics calculator: i graph the two functions on th ...

Part 5: Graphs of the form y=a(x¡h)^2 +k, a 6 =0 What to do: 1 Without the assistance of technology, sketch the graphs of y=2x^2 ...

2 y x @\=\(!\+\2)X\-\5 @\=\!X 55 O + 2 + 3 y x @\=\(!\-\2)X\+\3 @\=\!X O Example 11 Self Tutor Sketch y=x^2 and y=x^2 +3 ...

y x + 2 3 @\=\-(!\-\2)X\-\3 @\=\-!X @\=\!X ()2 -3, OO x y @\=\!X @\=\3!X @\=\-3!X OO Example 13 Self Tutor Sketch y=x^2 on a s ...

EXERCISE 21E.3 1 On separate sets of axes sketch y=x^2 and each of the following functions. Comment on: i the shape of the graph ...

Given the equation of any curve: Anx-interceptis a value ofxwhere the graph meets the x-axis. x-intercepts are found by lettingy ...

Example 15 Self Tutor Find thex-intercepts of: a y=2(x¡3)(x+2) b y=¡(x¡4)^2 a When y=0, 2(x¡3)(x+2)=0 ) x=3 or x=¡ 2 ) thex-inte ...

x y 12 4 O 3 For the following functions, find thex-intercepts: a y=x^2 ¡ 9 b y=2x^2 ¡ 6 c y=x^2 +7x+10 d y=x^2 +x¡ 12 e y=4x¡ ...

EXERCISE 21F.2 1 Sketch the graph of the quadratic function with: a x-intercepts¡ 1 and 1 , andy-intercept¡ 1 b x-intercepts¡ 3 ...

Proof: We know the equation y=a(x¡h)^2 +k has vertex(h,k), so its line of symmetry is x=h. Expanding y=a(x¡h)^2 +k, we find y=a( ...

-2 6 x y x¡=¡2 2 O y x x= 1 3 -1 3 vertex(1' 4) @\=\-!X\+\2!\+3 O c Fromb, when x=1, y=¡(1)^2 + 2(1) + 3 =¡1+2+3 =4 ) the vertex ...

EXERCISE 21G 1 Determine the equation of the line of symmetry of: a y=x^2 +4x+1 b y=2x^2 ¡ 6 x+3 c y=3x^2 +4x¡ 1 d y=¡x^2 ¡ 4 x+ ...

Example 24 Self Tutor Find the quadratic function with: a vertex(1,2)andy-intercept 3 b vertex(2,11)which passes through the poi ...

3 For each of the following graphs, find the function they represent in the form y=a(x¡h)^2 +k. abc 4 Find the quadratic functio ...

Example 26 Self Tutor Solve 2 x^2 ¡ 3 x¡4=0 using technology, giving your answers correct to 3 decimal places. Consider y=2x^2 ¡ ...

Example 27 Self Tutor The sum of a number and its square is 42. Find the number. Let the number bex. Therefore its square isx^2. ...