Graph Quadratic Functions
Graph Quadratic Inequalities
Solve Quadratic Equations Algebraically
Solve Quadratic Equationsby Factoring
Solve Quadratic Equationsby Graphing
Liberty University
Findthe Minimumand Maximum Values


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so we know when we have grass we've talked about. When you have a graph of a quadratic function, you have a parabola and you have two types of parabola. You have one that opens up and you have one that opens down now and one that opens up. This is where you're a is greater than zero. Or, in other words, you're term that comes before your eggs square is positive in a good way to remember. That is, when you're in a positive mood, you're happy. So you're faces smiling. So here you have a smiling face. So it's a positive is going upwards when you have one that's going downwards. This is when you're a term is less than zero. Meaning you have a negative term in front of your X square, your coefficients negative. And you can kind of remember this. You can think of a sad day when you're feeling negative or feeling bad. You're kind of frowning, so your arrival is kind of making this frowny face. It's just kind of a quick way to remember these or dealing with minimum and maximum. What we're talking about is we're looking for that highest or lowest spot on the parabola. So, for example, when I have a positive, I'm looking for that lowest spot. So they're here. You have a minimum value when I have a negative. I'm looking for a maximum because here, because my parabola is going down, I have a highest value. So you're looking for kind of where which one is the highest or which one is the lowest? As faras working them out, though, you're gonna be looking for the same thing. And what you're gonna do is you're going to start off by finding the X coordinate of the Vertex. Which way said was the axis of symmetry. So you're going to use the formula X equals negative, be over to a and then you'll find the why coordinate of that and that why coordinate is going to be your minimum or your maximum. So let's look at a few equations. Let's look at the one f of X equals X squared minus four X plus nine. Well, we know we have three sets of coordinates. We have a a coordinate, which is gonna be one. We have a B coordinate, which is negative four and a C coordinate which is none were gonna be focused on this. Be coordinate this negative four. And we're going to start off by finding the X coordinate of the Vertex. So for this one, remember, we're gonna use negative, be over to a So for this, we're gonna have negative negative four over to times one. So we're gonna have a positive 4/2. So our X coordinate is going to be too. Well, now that I know my X coordinate is too in place of the exes, I'm gonna plug two to find. What my Y coordinate ISS. So I'm gonna have to squared minus four times two plus none. So we'd have four minus eight plus nine, and that is going to give me five. So the y coordinate of either my minimum I max, someone is five. Now, let's look, we said that we're looking either is the a term positive or is it negative? Well, in this case are a term is positive. So that means because we're looking at positive, we're looking at a minimum value, so our minimum equals positive. Let's look at the quadratic equation. Are quadratic function of of X equals negative X square minus nine and we're gonna find the minimum or maximum value. Well, for this one are a term is going to be negative. One RB term, we don't have an X. So another way of writing this could be negative. X squared plus zero x minus time because you're be term has to be the coefficient of X. And since it's not in there, that means that it was zero. So my B term is zero, and my C is negative. Not well, since my A is negative, that means that we're looking for a He's gonna be a downward Perabo. Let's go open up, down. Which means we're looking at a maximum value. And so now we're gonna use the we're gonna find our X coordinates for a Vertex. And when you do that by going negative, be over to a well, for a B, A 00 is not gonna be negative or positive. So I'm just gonna put 0/2 times negative one so zero over negative to, which means that X is going to equal zero. So now that we know X equals zero, we can plug that back into our function. So we're gonna have negative zero squared minus non. Well, of course. Zero squared to zero and zero minus nine is negative. Nine. So that means our maximum value is going to be negative? None. So, actually, what's gonna end up happening is that when I graph this one, this one's actually gonna be a fairly low graph on my actual coordinate grid.

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