SOLUTION: Where does the graph of y = 2x^2 − x − 3 cross the x-axis? A. (−, 0) and (3, 0) B. (, 0) and (−3, 0) C. (−, 0) and (1, 0) D. (, 0) and (&#

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Question 582589: Where does the graph of y = 2x^2 − x − 3 cross the x-axis?
A. (−, 0) and (3, 0)
B. (, 0) and (−3, 0)
C. (−, 0) and (1, 0)
D. (, 0) and (−1, 0)

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Simply set y equal to zero and solve for x:

Start with the given equation


Plug in y = 0


Flip the equation.


Notice that the quadratic is in the form of where , , and


Let's use the quadratic formula to solve for "x":


Start with the quadratic formula


Plug in , , and


Negate to get .


Square to get .


Multiply to get


Rewrite as


Add to to get


Multiply and to get .


Take the square root of to get .


or Break up the expression.


or Combine like terms.


or Simplify.


So the solutions are or


This means that the x-intercepts are (3/2, 0) and (-1, 0). These are the points where the graph crosses the x-axis.


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