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≥ 2 }
We want to graph the given quadratic function.
y=x^2+4x+6
To do so, we will first make a table of values.
| x | x^2+4x+6 | y=x^2+4x+6 |
|---|---|---|
| - 4 | ( - 4)^2+4( - 4)+6 | 6 |
| - 3 | ( - 3)^2+4( - 3)+6 | 3 |
| - 2 | ( - 2)^2+4( - 2)+6 | 2 |
| - 1 | ( - 1)^2+4( - 1)+6 | 3 |
| 0 | ( 0)^2+4( 0)+6 | 6 |
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 2. Using this information, we can write the domain and range of the function. Domain:& { all real numbers } Range:& { y | y≥ 2 }