1. Graphing f(x) = ax^23
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Make a table to find points on the curve. Then plot and connect the points.
Graph:
Comparison to the graph of f(x)=x^2: There is a vertical stretch by a factor of 92 followed by a reflection in the x-axis of the graph of f.
To graph the function we will make a table of values.
| x | - 9/2 x^2 | q(x)=- 9/2 x^2 |
|---|---|---|
| - 4/3 | - 9/2( - 4/3)^2 | - 8 |
| - 1 | - 9/2( - 1)^2 | - 4.5 |
| 0 | - 9/2( 0)^2 | 0 |
| 1 | - 9/2( 1)^2 | - 4.5 |
| 4/3 | - 9/2( 4/3)^2 | - 8 |
Let's now draw the parabola that connects the obtained points. We will also draw the parent function f(x)=x^2.
From the graph above, we can note the following.
From the graph and the observations above, we can conclude that the graph of q is a vertical stretch by a factor of 92 and the reflection in the x-axis of the graph of f.