Graph parabolas :
To graph a parabola, first we need to find the following things one by one.
After finding the above mentioned points, we can graph a parabola easily.
How to know the axis of symmetry of a parabola ?
The parabola is symmetric about the variable, which is not having square.
Example :
In the equation of the parabola y² = 16x, the variable x is not having square and also it has power 1.
Hence the parabola represented by the equation y²= 16x, is symmetric about x-axis.
How to find the vertex of the parabola ?
To find the vertex of the parabola, we have to compare the given equation with the anyone of the following equation depending on the axis of symmetry and the side which it is open.
How to find x and y-intercepts of the parabola ?
Let us see some more example problems based on the above concept.
Example 1 :
Graph the parabola (y - 1)² = 8 (x - 2)
Solution :
The given equation exactly matches the equation
(y - k)² = 4a (x - h)
Axis of symmetry :
Here the variable x is not having square, so it is symmetric about x axis. Since 8 is positive, it is open rightward.
Vertex :
By comparing the given equation with the general form, we get vertex
(y - k)² = 4a (x - h)
(y - 1)² = 8 (x - 2)
Vertex (h, k) ==> (1, 2)
x and y-intercept :
To find x-intercept put y = 0 (0 - 1)² = 8 (x - 2) 8(x - 2) = 0 x - 2 = 0 add 2 on both sides x = 2 (2, 0) |
To find y-intercept put x = 0 (y - 1)² = 8(0 - 2) (y - 1)² = -16 There is no y-intercept. |
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