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Liberty University
Graph Quadratic Functions - Example 3


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Video Transcript

f of X equals X square plus four. Now here, this looks like a different kind of quadratic because we only have two terms. Well, that's because a lot of times you don't have to put that third term. If your coefficient is zero, another way of writing this one would be f of X would equal X squared plus zero X plus four. But since we know that zero times any number is zero ah, lot of times they'll drop a term if the coefficient is zero. But let's keep this one right here so we can kind of see and as we look. So let's start off by finding our Y intercept. Well, we can use our c term for that, which is going to be zero four. So why intercept is actually going to be four? From here, we can find our access to symmetry. So we're gonna look for our eggs and remember, that is be over negative to a So in this case, that would be zero over negative two times one or zero over negative too. Which would be zero. Well, I've already actually got X zero because that's my Y intercept. So we can see that our axis of symmetry or Vertex and our Y intercept are all gonna be 04 So at this point, I can tell that my this is the point that my parable is gonna change directions. Let's get a couple of other things. One since that term right there is positive already know that my parabola is gonna be an open direction. So that tells me that as I'm doing this since this is also gonna be my axis of symmetry, I need to look for some X values that are both positive and negative. So let's look at some Let's just start with some basics. Let's start with positive one. So that would be one square plus four, which would be one plus four, which is going to give me five. And then let's do positive, too. So two squared plus four, which would be four plus four, would give me eight. Well, since we've got a couple of positive, let's do a couple of negatives. Let's do negative one. So that would be negative. One squared plus four, which would still be one plus four, which again would give me five. And then let's do negative, too. Negative. Two squared plus four would be a positive four plus four, which it again would give me eight. So now that we've got some points and I can kind of see a pattern as it's going, let's go ahead and graft these. I'm gonna list my point. So we have positive 15 positive to eight. Negative. 15 and negative to eight. So we'll start with our one and then five, and then to eight. Negative. 15 and negative, too. Eight. So right here, you can see is my parabola.