1. Graphing Quadratic Functions
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Make a table of values and connect the obtained points with a parabola.
Graph:
Domain: All real numbers
Range: y≥ -13
We want to graph the given quadratic function.
y=2x^2-8x-5
To do so, we will make a table of values.
| x | 2x^2-8x-5 | y=2x^2-8x-5 |
|---|---|---|
| -1 | 2( -1)^2-8( -1)-5 | 5 |
| 0 | 2( 0)^2-8( 0)-5 | -5 |
| 2 | 2( 2)^2-8( 2)-5 | -13 |
| 4 | 2( 4)^2-8( 4)-5 | -5 |
| 5 | 2( 5)^2-8( 5)-5 | 5 |
Let's now plot the obtained points on the coordinate plane and connect them with a parabola.
We see above that the x-variable can take any value. Conversely, the y-variable only takes values greater than or equal to -13. Using this information, we can write the domain and range of the function.
Domain:& all real numbers
Range:& y≥ -13