There, so 2 comma 2, and then you have a negative 2 comma 2.
SOLVING SYSTEMS BY GRAPHING PLUS
Negative there, so it's negative 4 plus 6 is 2. Square it, then you have positive 4, but you have a So when x is 2, what is y? You have 2 squared, which isĤ, but you have negative 2 squared, so it's negative 4 X is equal to- let me just draw a little table here. Graph a couple of other points, just to see The vertex of this parabola is when x is equal to 0,Īnd y is equal to 6. Thing can take on is when x is going to be equal to 0. When you multiply it by a negative, so it's going This whole term right here isĪlways going to be negative, or it's always going Its maximum point? Let's think about thatįor a second.
Opening parabola? You see that it's a negativeĬoefficient in front of the x squared, so it's going to be aĭownward opening parabola. It is going to be upward opening, or downward Know it's a parabola? That's because it's a quadraticįunction: we have an x squared term, a secondĭegree term, here. Is this going to be an upward opening- one, how did I Let's start- let me find a nice dark color to Here is a great on line graphing tool where you can experiment and get to know the properties of quadratic equations: Īlgebraically. Typically, one of the first things we do is set x=0 and see what value the function produces. With more practice, these properties will become part of what you know. Can you see how ANY other value of x will produce a value less than 6? (no matter what x is if it is not equal to zero it will be a negative number which means you will be taking away the negative number from 6. That means the maximum point at most can be 6 and that only happens when x=0 :: y=-x² + 6 = -0² + 6 = 0 + 6 = 6. that means that we will have the case that the equation will be something like this: a negative number + 6. So now our goal is to figure out what value of x produces the maximum point.ĪLL values of -x² are negative. That means the graph will have a maximum point. So no matter what value x has -x² will produce a negative number.įrom that, we know that as x gets bigger and bigger, -x² will produce and even bigger negative number, which means the graph goes further and further down into the negative area of the graph.įrom that we now know that the graph is concave down (kind of like the letter n, whereas concave up us more like the letter u).
The function is a member of the family of quadratic equations since the highest degree is 2.Īll quadratic equations produce a parabola as a graph. The equation under consideration is y=-x² + 6, so let's take a look at it and see if we can do some basic analysis to figure out what properties the graph might have. This would give us ?y? or ?-y? in both equations, which will cause the ?y?-terms to cancel when we add or subtract.What you call the turning point we call a maximum or a minimum point, which as you observed is where the graph changes direction or turns.
This would give us ?x? or ?-x? in both equations, which will cause the ?x?-terms to cancel when we add or subtract.ĭivide the first equation by ?3?.
This would give us ?3y? or ?-3y? in both equations, which will cause the ?y?-terms to cancel when we add or subtract.ĭivide the second equation by ?2?. Multiply the second equation by ?3? or ?-3?. This would give us ?2x? or ?-2x? in both equations, which will cause the ?x?-terms to cancel when we add or subtract. Multiply the first equation by ?-2? or ?2?. So we need to be able to add the equations, or subtract one from the other, and in doing so cancel either the ?x?-terms or the ?y?-terms.Īny of the following options would be a useful first step: When we use elimination to solve a system, it means that we’re going to get rid of (eliminate) one of the variables. To solve the system by elimination, what would be a useful first step?
SOLVING SYSTEMS BY GRAPHING HOW TO
How to solve a system using the elimination method
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