# What are the important points needed to graph f(x)= x^2 + 1?

Jul 29, 2018

See explanation for more.

#### Explanation:

When drawing a graph such as $f \left(x\right)$ you pretty much only need to find the points for where $f \left(x\right) = 0$ and the maxima and minima and then draw the lines between these.

For example, you could solve $f \left(x\right) = 0$ by using the quadratic equation. To find the maxima and minima you can dervivate the function and find $f ' \left(x\right) = 0$.

$f \left(x\right) = {x}^{2} + 1$ does not have any points for where the function is zero. But it has a minimal point located at $\left(0 , 1\right)$ which can be found through $f ' \left(x\right) = 0$.

Since it's harder to know how the graph is illustrated without the points where $f \left(x\right) = 0$, and without maxima and minima we can add a table for the graph. Which we can do with a set of random $x$ values. In order to see the $f \left(x\right)$ values at the $x$ values.

You can view a method for this here.