We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
289
1
avatar

Two parabolas are the graphs of the equations $y=3x^2+4x-5$ and $y=x^2+11$. Give all points where they intersect. List the points in order of increasing $x$-coordinate, separated by semicolons.

 Jun 17, 2018
 #1
avatar+8167 
+2

A point of intersection is a point that makes both equations true.

 

y  =  3x2 + 4x - 5       and       y  =  x2 + 11

 

Starting with the first equation...
 

y  =  3x2 + 4x - 5

                                       Since  y  =  x2 + 11  we can substitute  x2 + 11  in for  y .

x2 + 11  =  3x2 + 4x - 5

                                       Subtract  x2  from both sides of the equation.

11  =  2x2 + 4x - 5

                                       Subtract  11  from both sides of the equation.

0  =  2x2 + 4x - 16

                                       Divide through by  2 .

0  =  x2 + 2x - 8

                                       Factor the right side.

0  =  (x - 2)(x + 4)

                                       Set each factor equal to zero and solve for  x .

 

x - 2  =  0          or          x + 4  =  0

 x  =  2              or             x  =  -4

 

Use these values of  x  to find  y .

 

If    x  =  2    then    y  =  (2)2 + 11  =  4 + 11  =  15    So   (2, 15)  is a point of intersection.

 

If    x  =  -4    then    y  =  (-4)2 + 11  =  16 + 11  =  27    So   (-4, 27)  is a point of intersection.

 

The points of intersection are   (-4, 27)   and   (2, 15) .

 Jun 18, 2018

14 Online Users

avatar
avatar
avatar