This week in Pre-Calc we finished up our quadratic functions unit. In this blog post I am going to show how you can look at a graph and figure out the equation. For this blog post I am going to focus on how to put it into the vertex form of the equation.
For this blog post I am going to use this graph as example:
Step 1: So to start off with I am going to look at the vertex. I know that my x value of the coordinate (5) is going to be inserted into the equation, In the position (x-5). But we need to flip the sign to negative. If we started with a negative it would flip to positive.
Step 2: Now I can take my 2, from the y part of the coordinate and add +2 after my bracket, to show it is going to have a vertical translation of +2 when you graph it.
Step 3: We have inserted all of the information we can from our vertex, we are going to need to use the given point to find our stretch. To do this we have to insert the x and the y values from our coordinate into the equation where there is an x or a y. So in this case our coordinate is (3,-2). so the -2 is going to replace y=, and the 3 is going to replace the x in the bracket. But if you go back and look at the original graph, it was congruent to the parent function, meaning there isn’t a stretch.
Step 4: The final thing we have to do is notice the parabola is a maximum so there has to be a negative out front of the bracket.
I’ll do an example on how to find the stretch. Let’s say we found the first part of our equation and the points given to us are, (-1,-13).
Step 1: The first step is to insert our x and y values, like I explained above. Put the -1 in where the x is, and -13 where y is. I am going to put a in front of our bracket to represent the stretch.
Step 2: Now we have to solve this equation. I am going to start with inside the bracket and clean that up.
Step 3: Now I am going to square the 2. And add 5 to both sides to get rid of the -5, as it can’t be added to the 4a.
Step 4: My final step is to divide -8, by 4 because I have isolated the variable. When I do this I can see my parabola has a stretch of -2.
And that is what you need to know on how to look at a graph and put it into vertex form.
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