## Code

```
<- function(x) {
f ^2 - 11*x + 28
x }
```

We know what a quadratic equation is:

\[ ax^2 + bx + c = 0 \]

But what if we could actually *see* the answers, plotted out in a graph?

Before we can plot anything, we need an equation.

We will be plotting 4 equations. Here they are:

- \(x^2 - 11x + 28\)
- \(x^2 - x + 46\)
- \(x^2 + 49\)
- \(x^2 -4x\)

We need to make a function first. We will use variables f, g, h, and k for our functions. Here’s how you make a function:

Let’s break down each part of the function. The `function(x)`

part is the number we will plug in, it is the same as writing \(f(x)\). Now, what does \(f(x)\) equal? That is the part that goes in the curly brackets. We also want to save it to an object `f`

.

This:

Is the same thing as this:

\[ f(x) = x^2 - 11x + 28 \]

Here’s what the rest of the functions are written in code:

And here they are not in code; \(g(x) = x^2 - x + 46\), \(h(x) = x^2 + 49\), \(k(x) = x^2 - 4x\)

Now that we have all of our functions written out, we can plug any number in for \(x\)

```
---
title: "Plotting Quadratic Equations"
subtitle: "Functions"
# date:
categories: [math]
# image:
format:
html:
code-fold: show
code-tools: true
---
We know what a quadratic equation is:
$$
ax^2 + bx + c = 0
$$
But what if we could actually *see* the answers, plotted out in a graph?
\
## Some equations
Before we can plot anything, we need an equation.
We will be plotting 4 equations. Here they are:
- $x^2 - 11x + 28$
- $x^2 - x + 46$
- $x^2 + 49$
- $x^2 -4x$
## Making Functions
We need to make a function first. We will use variables f, g, h, and k for our functions. Here's how you make a function:
```{r, function-f}
f <- function(x) {
x^2 - 11*x + 28
}
```
### What's going on here?
Let's break down each part of the function. The `function(x)` part is the number we will plug in, it is the same as writing $f(x)$. Now, what does $f(x)$ equal? That is the part that goes in the curly brackets. We also want to save it to an object `f`.
This:
```{r, function}
f <- function(x) {
x^2 - 11*x + 28
}
```
Is the same thing as this:
$$
f(x) = x^2 - 11x + 28
$$
## All of the other functions
Here's what the rest of the functions are written in code:
``` {r, function-g-h-k}
g <- function(x) {
x^2 - x + 46
}
h <- function(x) {
x^2 + 49
}
k <- function(x) {
x^2 -4*x
}
```
And here they are not in code; $g(x) = x^2 - x + 46$, $h(x) = x^2 + 49$, $k(x) = x^2 - 4x$
## Let's graph!
Now that we have all of our functions written out, we can plug any number in for $x$
```