SOLUTION: Ok so I have been stuck on how to figure out vertex of a parabola and the maximum/minimum. I know that if it is a negative number then we should look at maximum. I have a TI-83 cal

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Ok so I have been stuck on how to figure out vertex of a parabola and the maximum/minimum. I know that if it is a negative number then we should look at maximum. I have a TI-83 cal      Log On


   

Question 151599: Ok so I have been stuck on how to figure out vertex of a parabola and the maximum/minimum. I know that if it is a negative number then we should look at maximum. I have a TI-83 calculator but I can't even begin to figure out, if I could do this on the calculator. Here is one example from my book:
-.2x^2+1.4x-5.9
Any help would be so appreciated. I need to know how to break down this problem in "dumb terms". I look at the book and I get even more confused. Thank you, Thank you, Thank you
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
In order to find the vertex with a calculator, first graph y=-0.2x%5E2%2B1.4x-5.9. Now press 2nd and then "trace". This will lead you to the "calc" menu. Now scroll down to "maximum" and hit enter. Find the highest point on the graph and scroll slightly to the left and hit enter. Now scroll past the highest point and go slightly to the right and hit enter. Finally hit enter a third time to let the calculator find the max. Let me know if you have a problem with any of these steps.

Here's a good tutorial to find the maximum.

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Here's how to find the vertex algebraically (ie without a graphing calculator)


In order to find the vertex, we first need to find the x-coordinate of the vertex.


To find the x-coordinate of the vertex, use this formula: x=%28-b%29%2F%282a%29.


x=%28-b%29%2F%282a%29 Start with the given formula.


From y=-0.2x%5E2%2B1.4x-5.9, we can see that a=-0.2, b=1.4, and c=-5.9.


x=%28-%281.4%29%29%2F%282%28-0.2%29%29 Plug in a=-0.2 and b=1.4.


x=%28-%281.4%29%29%2F%28-0.4%29 Multiply 2 and -0.2 to get -0.4


x=3.5 Divide -1.4 and -0.4 to get 3.5


So the x-coordinate of the vertex is x=3.5. Note: this means that the axis of symmetry is also x=3.5.


Now that we know the x-coordinate of the vertex, we can use it to find the y-coordinate of the vertex.



y=-0.2x%5E2%2B1.4x-5.9 Start with the given equation.


y=-0.2%2A%283.5%29%5E2%2B1.4%283.5%29-5.9 Plug in x=3.5


y=-0.2%2812.25%29%2B1.4%283.5%29-5.9 Square 3.5 to get 12.25.


y=-2.45%2B1.4%283.5%29-5.9 Multiply -0.2 and 12.25 to get -2.45.


y=-2.45%2B4.9-5.9 Multiply 1.4 and 3.5 to get 4.9.


y=2.45-5.9 Add -2.45 and 4.9 to get 2.45.


y=-3.45 Subtract 5.9 from 2.45 to get -3.45.



So the y-coordinate of the vertex is y=-3.45.


This means that the vertex is .