Sketching graphs looks hard but if you follow the rules carefully they can be very easy.
| Sketching Quadratic Equations
example : x2 +2x -3 | Co-efficients
First we need to note the co-efficients a, b and c
a is the co-efficient of x2 - in the example above a = +1
b is the co-efficient of x - in the example above b = +2
c is the co-efficient of the Y intercept - in the example above c = -3 | Shape
The shape of the graph will be either "U" or "n"
This is determined by the co-efficient of a
if a is negative then it is "n" shaped (easy to remember negative = "n")
If a is positive then it is "U" shaped | Location
Quadratic graphs are symetrical (the left and right halves are identical)
To find the centre line we can use the formula
-b/2a
So in our example the centre line is at x = -2/2(1) = -1
So the graph will be formed around the centre line at x = -1
When x = -1, y = -12 + 2(-1) -3 = -4
This will be where the lowest point of the U shape is i.e. (-1, -4)
We know it is U shaped because the co-efficient a is positive | Intercepts
The Y intercept is at co-efficient c - so the graph cuts the Y axis at -3
The X intercepts (if there are any) must be found by factorising the equation.
x2 +2x -3 = (x + 3) (x - 1)
so x = +1 or -3 when y = 0 | Draw
It is now a simple matter to draw A "U" shaped graph
Where the lowest point is at (-1,-4)
Cutting the x axis at -3 and +1
(and as a double check - cutting the y axis at -3)
Done !! |
| notes
A "normal" is another name for a perpendicular line from a tangent.
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