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Volume: Coordinate Geometry
Get Your Basics Right! Foundation Course
Lesson Graphing Quadratic and Higher Relations
Video Lesson – You-Tube Link
https://youtu.be/dImTRExjYWw
The Course "Get Your Basics Right" will focus on Basic
Mathematics and Science Topics you should have mastered during
your high school. This course will help you see how to integrate
Mathematics with Sciences.
Learn everything you wanted to but couldn't! All those times you
caught yourself saying "I should have learnt this". This is your time in
hand to go ahead and actually learn it. This will help you stay ahead!
www.laddereducation.com
Ladder Educational Services
“Get Your Basics Right” | Vol # 1: Co-ordinate Geometry | Lesson: Graphing Quadratic and Higher Relations
1 Log-on to: www.laddereducation.com & Download the Worksheet 2 Learn through the Video lectures & Try Solving it
3 Work-along with on-line interactive class
Video Lesson
Q1. Why equation of the form 2 0ax bx c+ + = is named Quadratic? Q2. What pattern do you observe in the following relations?
2
3 2
4 3 2
5 4 3 2
00
00
y mx cax bx cax bx cx dax bx cx dx eax bx cx dx ex f
= +
+ + =
+ + + =
+ + + + =
+ + + + + =
Q3. Using GeoGebra, Plot the graph 2y x= and compare the graph with the following equations. 2
2
2
2
22
( 2)( 2)
y xy xy xy x
= +
= −
= +
= −
____________________________________________________________________________________________________________________ Practice Questions Q1. How do you compare the Graphs of the equation ny x= , for all possible values of n?
Q2. Using GeoGebra, draw the graph of 2 4 3y x x= − + for values of x from -1 to 5 inclusive and compare the
same with the graph 2 4 3y x x= − + − .
Q3. In the following set of equations, using GeoGebra, (a) draw a graph using the indicated value of x, (b) mark the
turning point with the letter T and state whether it is a minimum or a maximum point, (c) state the coordinates of the
turning point and (d) draw the axis of symmetry and state its equation: 2
2
2
2
2
2
(1) from 5 to 5(2) 2 from 2 to 2(3) 3 from 2 to 2(4) 9 from 4 to 4(5) 4 from 3 to 3(6) 4 from 2 to 6
y x x xy x x xy x x xy x x xy x x xy x x x x
= = − = +
= − = − = +
= = − = +
= − = − = +
= − + = − = +
= − = − = +
2
2
2
2
2
2
(7) 6 8 from 0 to 6(8) 6 8 from 0 to 6(9) 3 2 from 1 to 4(10) 2 from 2 to 3(11) 2 5 2 from 1 to 4(12) 2 7 3 from 0 to 4
y x x x xy x x x xy x x x xy x x x xy x x x xy x x x x
= − + = = +
= − + − = = +
= − + = − = +
= − + + = − = +
= − + = − = +
= − + − = = +
Q4. Sketch the graphs of the given equation and explain how a change from one equation to another changes the graph 2 2 2
2 2 2
2 2 2
2 2 2
(1) ; 2 ; 101 1(2) ; ; 2 10
(3) ; 2 ; 101 1(4) ; ; 2 10
y x y x y x
y x y x y x
y x y x y x
y x y x y x
= = =
= = =
= − = − = −
= − = − = −
2 2
2 2
2 2
2 2
(5) 3; 3(6) 2 4 ; 2 6(7) 3 2 1; 3 2 1(8) 2 1; 2 1
y x x y x xy x x y x xy x x y x xy x x y x x
= + + = + −
= + = +
= + + = − + +
= + + = − −
Q5. In the general equation 2y ax bx c= + + , What effect on the parabola does the change in a, b and c have?
