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 (&#

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> 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 (&#      Log On


   

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

y=2x%5E2-x-3 Start with the given equation


0=2x%5E2-x-3 Plug in y = 0


2x%5E2-x-3=0 Flip the equation.


Notice that the quadratic 2x%5E2-x-3 is in the form of Ax%5E2%2BBx%2BC where A=2, B=-1, and C=-3


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


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%282%29%28-3%29+%29%29%2F%282%282%29%29 Plug in A=2, B=-1, and C=-3


x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%282%29%28-3%29+%29%29%2F%282%282%29%29 Negate -1 to get 1.


x+=+%281+%2B-+sqrt%28+1-4%282%29%28-3%29+%29%29%2F%282%282%29%29 Square -1 to get 1.


x+=+%281+%2B-+sqrt%28+1--24+%29%29%2F%282%282%29%29 Multiply 4%282%29%28-3%29 to get -24


x+=+%281+%2B-+sqrt%28+1%2B24+%29%29%2F%282%282%29%29 Rewrite sqrt%281--24%29 as sqrt%281%2B24%29


x+=+%281+%2B-+sqrt%28+25+%29%29%2F%282%282%29%29 Add 1 to 24 to get 25


x+=+%281+%2B-+sqrt%28+25+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%281+%2B-+5%29%2F%284%29 Take the square root of 25 to get 5.


x+=+%281+%2B+5%29%2F%284%29 or x+=+%281+-+5%29%2F%284%29 Break up the expression.


x+=+%286%29%2F%284%29 or x+=++%28-4%29%2F%284%29 Combine like terms.


x+=+3%2F2 or x+=+-1 Simplify.


So the solutions are x+=+3%2F2 or x+=+-1


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