# What are the steps using a graphing calculator, to determine the max or min value of y=5.2sin(4x+80)+7.3?

What are the steps using a graphing calculator, to determine the max or min value of y=5.2sin(4x+80)+7.3

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First thing you have to do is plug the equation into your calculator. hit the green diamond, then F1 on the top left and you'll be in graphing mode. Type in the equation making sure to use correct parentheses.

Next, hit the green diamond and then F3, which will graph the equation. Now you may need to adjust the window. To do this, hit the green diamond and then F2. It should show you a list and the first item will be "xmin" which I would set to -5. The next item below that is xmax which I would set to 5. Skip over xscl, it's not important. ymin should probably be -15 and ymax should be 15. Once you've finished adjusting the window, hit the green diamond and F3 again to regraph it

To find a maximum or minimum, go to F5 and choose either option 3: Minimum or option 4: Maximum

It will ask you for a lower and upper bound. Making sure that you are following the graph, hit the left and right arrow keys until you are close to whichever "peak" (max or min) you are trying to find. Once you get close but it hasn't yet peaked, hit enter as this is your lower bound. Then scroll forward until the peak has passed (but you haven't encountered another peak) and hit enter for the upper bound. Give the calculator a second and there you go! It should give you the x,y coordinate of the answer

Source(s): AP Calculus AB class
• I'm not sure why you would need a graphing calculator, but I'll do it both ways for you.

Without a graphing calculator:

Realize that sine maximizes at 1 and minimizes at -1. Replace sin(4x + 80) with 1 for the maximum and sin(4x + 80) with -1 for the minimum.

Maximum: f(x) = 5.2sin(4x + 80) + 7.3 = 5.2(1) + 7.3 = 12.5

Minimum: f(x) = 5.2sin(4x + 80) + 7.3 = 5.2(-1) + 7.3 = 2.1

Therefore, the maximum value is 12.5 and minimum value is 2.1.

With a graphing calculator:

I'll show you the steps that I would use on my TI-84 Plus Silver Edition. Most people in Precalc have similar calculators so it (or some variation of these steps) should work for you.

Step 1: Go to "Y=" and type in 5.2sin(4x + 80) + 7.3 for "Y1=" at the top.

Step 2: Go to "WINDOW." Change the window so the graph is easily viewable. From what we discovered above, change "Xmin = 0" and "Xmax = 5". Change "Ymin = 1.5" and Ymax" = 13." The x values don't matter at all, actually, but the y values do so the maximum and minimum values will be visible.

Step 3: Press "GRAPH."

Step 4: After it is done graphing, press "2ND," then "CALC" (which is on the "TRACE" button). Press "3: minimum" first. Once you set the bounds between a minimum dip, it will show the value "Y=2.1," which confirms our answer above.

Step 5: Similarly, press "2ND," then "CALC" again. Press "4: maximum" this time. Once you set the bounds between a maximum peak, it will show the value "Y=12.5," which also confirms our answer.

Notice that it was much easier to solve it without graphing just by noticing that sine maximizes at 1 and minimizes at -1.

• i'm no longer particular why you may desire a graphing calculator, yet i will do it both techniques for you. and not using a graphing calculator: understand that sine maximizes at a million and minimizes at -a million. replace sin(4x + 80) with a million for the optimal and sin(4x + 80) with -a million for the minimum. optimal: f(x) = 5.2sin(4x + 80) + 7.3 = 5.2(a million) + 7.3 = 12.5 minimum: f(x) = 5.2sin(4x + 80) + 7.3 = 5.2(-a million) + 7.3 = 2.a million hence, the optimal fee is 12.5 and minimum fee is two.a million. With a graphing calculator: i will tutor you the steps that i could use on my TI-80 4 Plus Silver version. maximum folk in Precalc have similar calculators so it (or some version of those steps) may provide you with the outcomes you want. Step a million: flow to "Y=" and kind in 5.2sin(4x + 80) + 7.3 for "Y1=" on the authentic. Step 2: flow to "WINDOW." change the window so the graph is really viewable. From what we got here upon above, change "Xmin = 0" and "Xmax = 5". change "Ymin = a million.5" and Ymax" = 13." The x values do not remember in any respect, actual, inspite of the indisputable fact that the y values accomplish that the optimal and minimum values will be seen. Step 3: Press "GRAPH." Step 4: After it really is performed graphing, press "2d," then "CALC" (it extremely is on the "hint" button). Press "3: minimum" first. once you placed the bounds between a minimum dip, it is going to tutor the linked fee "Y=2.a million," which confirms our answer above. Step 5: in addition, press "2d," then "CALC" back. Press "4: optimal" this time. once you placed the bounds between a optimal height, it is going to tutor the linked fee "Y=12.5," which also confirms our answer. word that it replaced right into a lot less complicated to unravel it without graphing basically by utilising noticing that sine maximizes at a million and minimizes at -a million.