SOLUTION: What are the $x$-coordinate(s) of all point(s) where the parabola $y = f(x)$ intersects the line $y = 0$? f(x) = 2x^2 - 13x + 20 - 5x^2 + 19x + 7. Your answer shoul

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Question 1209639: What are the $x$-coordinate(s) of all point(s) where the parabola $y = f(x)$ intersects the line $y = 0$?

f(x) = 2x^2 - 13x + 20 - 5x^2 + 19x + 7.

Your answer should be a list of numbers and should not include variable names, nor should it include $y$-coordinates.
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
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What are the x-coordinate(s) of all point(s) where the parabola y = f(x) intersects the line y = 0?

f(x) = 2x^2 - 13x + 20 - 5x^2 + 19x + 7.

Your answer should be a list of numbers and should not include variable names, nor should it include $y$-coordinates.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

(1)  Simplify  f(x) = 2x^2 - 13x + 20 - 5x^2 + 19x + 7 = -3x^2 + 6x + 27.



(2)  The intersection points of the parabola with the line y = 0

     are the points on x-axis where  -3x^2 + 6x + 27 = 0.

     In Algebra language, these points are called the roots of the equation

          -3x^2 + 6x + 27 = 0.

     In other terminology, these points are called  x-interception points.



(3)  So, your task is to solve this equation

          -3x^2 + 6x + 27 = 0.


     To simplify, divide both side by the common factor -3.  You will get an EQUIVALENT equation

           x^2 - 2x - 9 = 0.


     Apply the quadratic formula

            =  =  = .


(4)  So, the roots of the given equation are  

         =  = -2.162 (rounded)  and  =  = 4.162 (rounded).


     They are x-coordinates of the intersection points.

Solved, with all necessary explanations.



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