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Question 116777: find the real roots of the equation by graphing: y=2x^2+2x-4
Found 2 solutions by jim_thompson5910, bucky:
Answer by jim_thompson5910(35256)   (Show Source):
Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! Given:
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y = 2x^2 + 2x - 4
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You can graph this equation by setting x equal to some value and then calculating the corresponding
value of y. Then plot the point (x, y) for each calculation.
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An easy one is to set x equal to zero. When you do, the equation reduces to:
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y = 0 + 0 -4 = -4
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So now you know that the point (0, -4) is on the graph. Plot it.
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Next you might let x = +1. This makes the equation:
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y = 2 + 2 - 4 = 0
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This means the point (1, 0) is on the graph. Keep doing this for convenient values of x,
both positive values and negative values. (The more (x, y) points you get, the more you will
be able to pinpoint the roots.
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The roots you are looking for are the values of x where the graph intersects the x-axis. There
are three possibilities ... the graph will cut across the x-axis at two points meaning that
there are two real roots. Or the graph will just touch or be tangent to the x-axis meaning
that there is only one real root. Or the graph will not touch or cut across the x-axis meaning
that there are no real roots.
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When you graph the given equation y = 2x^2 + 2x - 4 the graph will look like this:
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From this graph it appears that the roots are x = -2 and x = +1. If these answers are
correct you can plug them (one at a time) into the given equation for x and the corresponding
value of y should turn out to be zero.
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Hope this helps you to understand the problem, what it is asking you to do, and how you go
about getting the answer.
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