[MUSIC] Let's work with the equation of a quadratic function.

[SOUND] For example, let's find the equation of the quadratic function whose

graph passes through the point (-2,-1) and has a vertex at (-1,-3).

And then we'll put our answer in standard form.

Now, we have the following vertex form for the equation of a quadratic function,

f(x) = a * x - h quantity squared + k, where (h,k) is the vertex.

So here, we're given that the vertex is at (-1,-3), which means that h = -1 and k

= -3, which we can plug into this vertex form

here, which gives us that f(x) = a * x - -1 quantity squared + -3 or f(x) = a * x

+ 1 sqaured - 3. Now, it's [UNKNOWN] means to find a here

but we can use the fact that this point up here (-2 -1), lies on our graph in

order to help us find a. Because if (-2-1) lies on the graph, that

means that f(-2) = -1. So, we can plug in x = -2 and f(x) = -1 in our equation

here, and we will be able to find a.

Namely, -1 = a * -2 + 2 quantity squared - 3 or -1 = a * -1^2 - 3.

Which means that -1 = a - 3 or a = 2. And so, plugging this value of a into our

equation here gives us that f(x) = 2 * x + 1 quantity squared - 3.

Now, this is our equation. However, looking back up here, we're

asked to write our answer in standard form,

which we can do by squaring this out. Namely, f(x) = 2 * x^2 + 2x + 1 and then

minus 3. And now, distributing the two, we get

f(x) = 2x^2 + 4x + 2 - 3 or f(x) = 2x^2 + 4x -1, which is the equation we were

looking for in standard form. And this is how we find the equation of a

quadratic function given information about its graph.

Thank you and we'll see you next time. [MUSIC]