Make a table of values and connect the points with a parabola.
Domain: {all real numbers} Range: {y | y≥4 } Graph:
We want to graph the given quadratic function.
y=x^2+2x+5
To do so, we will first make a table of values.
x
x^2+2x+5
y=x^2+2x+5
2
2^2+2( 2)+5
13
1
1^2+2( 1)+5
8
0
0^2+2( 0)+5
5
- 1
( - 1)^2+2( - 1)+5
4
- 2
( - 2)^2+2( - 2)+5
5
- 3
( - 3)^2+2( - 3)+5
8
- 4
( - 4)^2+2( - 4)+5
13
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 4. Using this information, we can write the domain and range of the function.
Domain:& {All real numbers}
Range:& {y | y≥ 4 }
