okay in this video we're going to continue with quadratic functions and what we're going to focus on is finding that vertex we know that the the parabolas open up or down and i want to give you a few examples here let's take f of x equals a negative 3 times x minus 2 squared plus 12. now if you look back at the notes and let me just kind of flash that by here in the first video we had some notes that looked something like this and this is the form that we looked at it's called standard form i'm going to rewrite this back on this next page but the standard form is y equals or f of x equals a times x minus h squared plus k now these are the easiest kind of problems to find the vertex of because the vertex is simply h k the location of that vertex and let me let me reemphasize that one more time you look in that second video we had a picture that looked like this and the vertex is is the lowest point on a parabola that opens up off to the side here if we have a parabola that opens down the vertex is the highest point and what we're doing in these problems is locating where is what what are the coordinates of that vertex now in this problem we notice that the a value is negative a corresponds to this value it's negative so we know that the parabola is going to open down but it's vertex which is what we're concerned with is the h and k values h and k the h value it fits perfectly it's x minus h x minus h well the h value in this problem would have to be 2 and then the problem says you have a plus k plus k well the k value would be 12. so the vertex for this parabola that opens down this vertex point would be the coordinates 212. let me give you another example because these can get confusing with this minus and plus business but remember this is always standard form so let me give you another example this one says f of x equals or we could write y equals negative 2 times x plus 4 squared minus eight okay this negative value out here corresponds to the a in the formula if a is negative we know that the parabola opens down and what we're looking for right now at this point is just the vertex coordinate now the formula says x minus h well in this problem we have an x plus and you can't say that's h you have to write it as i'm going to rewrite it here x minus something because that's what's that's what the formula says x minus so x minus well what would that be it'd be minus a negative 4. okay plus k well that would be plus a negative 8. i know that's a crazy way to write that problem out but that gets the point across that this is my h value and this is my k value some students just look at it and say well i'll just remember that it's always the opposite of what i'm looking at here that's fine and and this k value here is always you take it at face value whatever that number is that's your k so let me answer it formally here the coordinates of the vertex the h value is negative four and the k value is negative eight let's practice one more of those just to make sure we've got it um f of x or y equals let's put in a five x plus three squared plus 2. well the 5 here tells me this is the a value and the a value says it opens up so what we're looking for the coordinates of that vertex that vertex is located at h k the h value is negative three because remember i'll rewrite it again it's x minus the h value and then the k value is just whatever this number is so the vertex is at negative three two okay now that's finding the vertex if the equation is in standard form the next video is going to say well how do we find the vertex if it's not in standard form so stay tuned for that one