explain how you would use graphing technology to find the solutions of 0 = −x^2 + 2.5x + 1. What do the solutions of 0 = −x^2 + 2.5x + 1 represent on the graph of the equation?
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I'm not quite sure what you're meaning by graphing technology, like a graphing calculator?
On a graphing calculator, press the y= button at the top left of the calculator.
enter in your equation -x^2+2.5x+1
then hit graph.
change the window so that you have a close up view of where y=0.
Now hit the 2nd Key and hit trace, which is calc in the 2nd key mode.
Once you do that, go down to where it says zero and press enter.
Then they're going to ask for a left bound and a right bound. Since there are two values of y=0, we're going to have to do this twice. We'll do the left value first. Move the cursor left until it is just barely underneath the y axis under where y=0. When it shows values, x and y should both be negative. Hit enter. Then it asks for right bound. Move the cursor to the right just a little bit until it shows x as negative and y as positive. It enter. Then it asks you to guess, just pick a random guess in between those two bounds, and press enter and voila, you have y=0 at -.3407811.
Now do the same procedure for the second value where y=0.
These numbers are the x-intercepts, where the graph intersects with the x axis.
On a graphing calculator, press the y= button at the top left of the calculator.
enter in your equation -x^2+2.5x+1
then hit graph.
change the window so that you have a close up view of where y=0.
Now hit the 2nd Key and hit trace, which is calc in the 2nd key mode.
Once you do that, go down to where it says zero and press enter.
Then they're going to ask for a left bound and a right bound. Since there are two values of y=0, we're going to have to do this twice. We'll do the left value first. Move the cursor left until it is just barely underneath the y axis under where y=0. When it shows values, x and y should both be negative. Hit enter. Then it asks for right bound. Move the cursor to the right just a little bit until it shows x as negative and y as positive. It enter. Then it asks you to guess, just pick a random guess in between those two bounds, and press enter and voila, you have y=0 at -.3407811.
Now do the same procedure for the second value where y=0.
These numbers are the x-intercepts, where the graph intersects with the x axis.
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This is the same as
x^2 - 2.5x - 1 = 0
How can you possible graph something that has only the x with no y or z?
There is only one solution and this is a point on the x axis approximately 2.85.
2.85^2 - 2.5(2.85) - 1 = - 0.003
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x^2 - 2.5x - 1 = 0
How can you possible graph something that has only the x with no y or z?
There is only one solution and this is a point on the x axis approximately 2.85.
2.85^2 - 2.5(2.85) - 1 = - 0.003
..
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- x^2 + 2.5x + 1 would be an n shaped graph(becauseof the - sign at the front)
The + 1 at the end is the y intercept (0,1)
Solve to find the x intercepts
Done on a calculator x = - 0.351 and x = 2.851
The + 1 at the end is the y intercept (0,1)
Solve to find the x intercepts
Done on a calculator x = - 0.351 and x = 2.851
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The solutions represent the values at which the graph intersects the x axis.