There is a graph of a quadratic equation shown, what function would match this graph?

Question

https://drive.google.com/file/d/19HSNlRbcxZP2qBTRpEigZTjF7xUOmybx/view?usp=sharing

i will point out that i do not know what a quadratic equation is

Answer 1

Hi Carsyn,

This is an excellent question. You must first realize that quadratic equations come in two forms: the standard form and the general form. The general form looks like this f(x)=ax²+bx+c and the standard form looks like this a(x-h)²+k.

The standard form is also called the vertex form. Please realize that the formulas look different but you can convert them to look like each other as long as they pertain to the same graph. Now on to the question:

The standard form is the best form to solve this type of problem. H is talking about the horizontal shift, left or right. K is talking about the vertical shift, up or down. This graph follows the standard form of an x² quadratic (the base template) but we notice that it is shifted 5 to the right so our h is 5 and it is shifted 4 below so our k is -4.

The formula is therefore: f(x) = (x-5)² - 4

This is the answer. But if you wanted to find the general formula, you can expand (x-5)(x-5) - 4 which gives you x²-10x+21.

Another way to solve it. You can look at the graph and find where it crosses the x axis. Notice how it crosses at x = 3 and x = 7. We would input that as (x-3)(x-7) and expand which gives us x²-10x+21. Now usually we would have to solve for a but we don't need to in this case. Our a is 1.

I realize talking about base templates may be confusing but it's an easier concept to explain in person or virtually. Reach out to me if you need more help.