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Title: How can you figure out if a graph is quadratic or exponential? Post by: Nuther Member on Nov 28, 2012 Well, i was out of school for a week and missed this lesson about determining if a graph was quadratic or exponential, and finding the equation for it. If the teacher gives you a few points on a graph, but it only shows half a parabola, or maybe all of the exponential, how can you determine the difference?
Also, how can you use this information and the points to find the equation for the graph. Title: How can you figure out if a graph is quadratic or exponential? Post by: smooth15 on Nov 28, 2012 Content hidden
Title: How can you figure out if a graph is quadratic or exponential? Post by: JulieA on Nov 29, 2012 If the points are consecutive, like (1,y1) (2,y2), (3,y3), etc, all you have to do to test if it's exponential is take y3/y2 then y2/y1 and see if the quotients are the same. If yes, then it's exponential. If not, you can test it as a quadratic by finding the second difference. This means find the average rate of change between each pair of points, then take the average rate of change of the average rate of changes. If those are constant then it's quadratic.
If the points are just random, like (1,y1), (5,y2), (12,y3), then you can test if it's exponential using ratios. An exponential equation is y=Ca^x. If you're given the vertical intercept, then this is very easy since you'll know C and will be able to substitute any of the coordinates to get the factor. Then it's simple to check the other given points to see if they work in that equation. If you don't have the vertical intercept, then you make a ratio of (y1=Ca^1)/(y2=Ca^5). Then you divide and end up with y1/y2=a^-4 (C cancels and you use exponent rules to combine a^1/a^5). Since you know what y1/y2 are (some constant), you raise both sides to the (-1/4) and you have a factor. You'll have to use this to find the C, but then once you have an equation, you can use this to check your other points. |