1. Graphing Quadratic Functions
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Make a table of values and connect the points with a parabola.
Graph:
Domain: { all real numbers }
Range: { y | y≥ - 8 }
We want to graph the given quadratic function.
y=3x^2-6x-5
To do so, we will first make a table of values.
| x | 3x^2-6x-5 | y=3x^2-6x-5 |
|---|---|---|
| - 2 | 3( - 2)^2-6( - 2)-5 | 19 |
| - 1 | 3( - 1)^2-6( - 1)-5 | 4 |
| 0 | 3( 0)^2-6( 0)-5 | - 5 |
| 1 | 3( 1)^2-6( 1)-5 | - 8 |
| 2 | 3( 2)^2-6( 2)-5 | - 5 |
| 3 | 3( 3)^2-6( 3)-5 | 4 |
| 4 | 3( 4)^2-6( 4)-5 | 19 |
Now, let's plot the obtained points and connect them with a parabola.
We can see above that the x-variable can take any value. Conversely, the y-variable only takes values greater than or equal to - 8. Using this information, we can write the domain and range of the function. Domain:& { all real numbers } Range:& { y | y≥ - 8 }