# Question #e1123

Dec 21, 2016

graph{x^2 - 5 [-15.8, 15.82, -7.9, 7.9]}

#### Explanation:

1) The key to graphing functions is to look at what I call the "mother function". In this case, the mother function is simply ${x}^{2}$.

2) The graph of ${x}^{2}$ is an upward parabola.

3) Now we also have $- 5$ after our ${x}^{2}$. That is always on your $y$-axis. So for $- 5$, you simply go down $5$ (down because it is $- 5$) and that is the apex/vertex of your parabola.

If it was, let's say, ${x}^{2} + 7$, you simply go up $7$ (because it is $+ 7$). So the sign determines whether you move the vertex up or down.

OR

You can graph it by plotting points which in my opinion takes unnecessary time, but here is how you do it:

1) write your equation $y = {x}^{2} - 5$

2) Plug in different values for $x$ and see what your $y$ becomes.

For example, plugging $0$ for $x$, you get

$y = {0}^{2} - 5$

So your $y$ is $- 5$. And that is what you see in the graph $\left(0 , - 5\right)$

Plugging $- 3$ for $x$ would give you

$y = {\left(- 3\right)}^{2} - 5$

which equals $4$. And so you have the point $\left(- 3 , 4\right)$ on your graph. And so on... You got the idea (:

3) but even with plotting points, the key is that you still need to know what your "mother functions" look like.

The graph of $y = {x}^{2}$ looks like a parabola, $y = {x}^{3}$ looks like an $\text{S}$, $y = x$ is just a straight line from negative infinity to positive infinity passing through the center of graph $\left(0 , 0\right)$, etc.

Hope it helped (c: