 In this video, we actually want to construct a quadratic function where we know its vertex is one comma negative five and its y-intercept is going to be zero comma negative three. Now having the vertex is the most valuable point on a parabola because given the vertex form f of x equals a times x minus h squared plus k, we can fill in the two parameters h and k immediately by using one for a to negative five for k. This gives us the formula f of x equals a times x minus one squared minus five. Now we just have to determine this leading coefficient a for which the y-intercept can help us out here because if the y-intercept is zero comma negative three, this tells us that f of zero is equal to negative three. So negative three, which is going to equal f of zero, using the formula here, we see that's equal to a times zero minus one squared minus five, which simplifies to be a times negative one squared minus five, which is going to be a minus five. That is summarizing a minus five equals negative three. If we then add five to both sides, a equals five minus three, which is equal to two. And so this tells us that our quadratic function y equals, well let's call it f of x, that's what it's called, f of x equals two times x minus one squared minus five, which if we want to, we could just leave it in the vertex form and this then gives us a function that has the behavior we want of this parabola. If you don't want a vertex form, we can multiply it out. We're going to get two times x squared minus two x plus one minus five, distribute the two, we get two x squared minus four x plus two minus five, and this equals two x squared minus four x minus three in that situation. So you could use this information right here if you want the standard form. Notice of course that if you have a quadratic function, let's say you have f of x equals a x squared plus b x plus c. Notice that this c right here is of course just going to be the y-intercept. This is a negative three right there. That's an observation that's very useful to hold here as well. So we can actually build a quadratic function with the information from its vertex with its y-intercept, and honestly you can see the vertex at any point on the parabola and we could have done something similar like this to find the coefficient a and get us a function for that quadratic function.