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Two parabolas are the graphs of the equations y=2x^2-7x+1 and y=8x^2+6x+1. Give all points where they intersect. List the points in order of increasing x-coordinate, separated by semicolons.

 Jun 28, 2022
 #1
avatar+124676 
+1

Set the equations equal

 

8x^2 + 6x + 1 =  2x^2 - 7x + 1          rearrange as

 

6x^2 + 13x   =  0       factor

 

x (6x  - 13)  = 0

 

The  x coordinates   are

 

x = 0                        and        6x - 13 = 0

                                                6x = 13

                                                   x  =13/6

 

 

When x = 0  y  =1

 

When x = 13/6, y=  2(13/6)^2 - 7(13/6) + 1   =  -43/9

 

The points of intersection are 

 

(0 , 1) , (13/6 , -43/9 )

 

 

cool cool cool

 Jun 28, 2022
 #2
avatar+2448 
0

Set equal: \(2x^2-7x+1 =8x^2+6x+1\)

 

Simplify: \(6x^2 + 13x = 0\)

 

Factor: \(x(6x + 13) = 0\)

 

If \(6x + 13 = 0\)\(x = -{13 \over 6}\), else \(x = 0\)

 

Substituting this into the quadratic, we find the points of intersection are \(\color{brown}\boxed{(-{13 \over 6},{ 43 \over 9}) \ \text{and} \ ({0, 1})}\)

 Jun 28, 2022

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