Welcome to another video from UltimateAlgebra.com. In this video, we will be looking at graphing Quadratics.

The graph of a quadratic is parabola. The basic formula for parabolas is y equals x squared. Let’s graph it.

We pick our x values from negative 2 to 2. We put the x values into the equation and find our y values.

 

When x is negative 2, we square the negative 2 to get y = 4

When x is negative 1, we square the negative 1 to get y = 1

When x is zero, we square the zero to get y = 0.

When x is 1, we square the 1 to get y = 1

When x is 2, we square the 2 to get y = 4.

 

Let’s bring our graph sheet. We plot our 5 points. Now we can graph our parabola through these points. Our graph will look like this. This is the basic graph of parabola. This is the vertex. It is the lowest point of this parabola. When the parabola is turned upside down, it becomes the highest point as we’ll see later.

So the basic quadratic equation gives this basic parabola, Everything else we add to the basic equation, just shifts the parabola or modifies it.

 

Let’s first look at what happens to our graph when we add or subtract.

Let’s say we have y equals x squared plus 1.

Let’s use our table to graph this. When x is negative 2, we will have negative 2 squared plus 1. Y is therefore 5. We’ll do the same for the rest to get these values for y.

2,1,2,5.

Let’s bring our graph sheet.

We plot our points.

 

This is the parabola of the basic quadratic equations. See what happens when we move it up 1. It passes through all our points. So we can say that when we add 1 to the basic quadratic equation then we will move the basic parabola 1 up.

With the same inference, when you add 2, you will move 2 up and so on.

 

When we subtract, we move down. Let’s look at y = x minus 2. We don’t even need the table. Let’s look straight at the graph. This is a basic parabola. We will move the basic parabola 2 down. So this will be the graph of the this equation.

 

Please note that we are normally just required to have a rough sketch of graphs here. So this graph could have just been represented simply this way. The most important thing is to show the shift.

 

Let’s look at a few more things.

Let’s look at left and right shifts. We start with our basic equation. Y = x squared. We know that this is the basic parabola for this equation.

If we have x + 1 squared. We will have a shift that is opposite the value here. So here we have a plus 1, so we will shift minus 1. That’s one to the left. We just need a rough graph that shows the shift.

 

Let’s look at y equals x minus 2 squared. Let’s bring our basic parabola. Here we move opposite what is here. We have negative 2, so we will move positive. Which means we will move 2 to the right. We know what to do. The shift will look like this.

 

It is possible to have multiple shifts in one graph. Example y = x plus 3 squared minus 2. Let’s bring our basic parabola. We can shift the graph 3 to the left first because of the plus 3, then shift it 2 down because of the negative 2. So this is the parabola for this quadratic equation.

 

Let’s end this video on that note. We will continue with Parabolas in the next video. Have a great day. Good bye