Practice test
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Make a table of values and connect the points with a parabola.
Domain: {All real numbers}
Range: {y | y≥ - 0.125 }
Graph:
We want to graph the given quadratic function. y=2x^2-3x+1 To do so, we will first make a table of values.
| x | 2x^2-3x+1 | y=2x^2-3x+1 |
|---|---|---|
| 4 | 2( 4)^2-3( 4)+1 | 21 |
| 3 | 2( 3)^2-3( 3)+1 | 10 |
| 2 | 2( 2)^2-3( 2)+1 | 3 |
| 0 | 2( 0)^2-3( 0)+1 | 1 |
| - 1 | 2( - 1)^2-3( - 1)+1 | 6 |
| - 2 | 2( - 2)^2-3( - 2)+1 | 15 |
Since we cannot easily determine the coordinates of the vertex, recall that a minimum value, is given by f ( - b2a ). Let's identify the values of a, b and c for our function. y=2x^2-3x+1 ⇕ y= 2x^2+( - 3)x+ 1 Before we find the value of the function at the vertex, we need to substitute a= 2 and b= - 3 in - b2a.
a= 2, b= - 3
Multiply
- - a/b= a/b
Calculate quotient
Now we have to calculate the value of the given function for x=0.75. To do so, we will substitute 0.75 for x in the given function.
x= 0.75
Calculate power
Multiply
Add and subtract terms
This tells us that the minimum value of the function is - 0.125. Therefore, the y-variable only takes values greater than or equal to - 0.125. Additionally, on the graph we can see that the x-variable can take any value. Using this information, we can write the domain and range of the function. Domain:& {All real numbers} Range:& {y | y≥ - 0.125 }