# In what quadrant does the curve y= x^2 -5x+3 meets the curve y= 2x^2 -3x +4

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

At the point where the two curves meet, the x and y coordinates are the same.

y = x^2 - 5x + 3 and y = 2x^2 - 3x + 4

Equate the two

x^2 - 5x + 3 = 2x^2 - 3x + 4

=> x^2 + 2x + 1 = 0

=> (x + 1)^2 = 0

=> x = -1

y = 2*1^2 + 3 + 4 = 2 + 3 + 4 = 9

The point of intersection is (-1 , 9).

The point of intersection lies in the second quadrant.

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given the curve y= x^2 - 5x + 3 and the curve y= 2x^2 - 3x + 4

We need to find the position of the intersection point.

First we will determine the coordinates of the intersection points.

==> 2x^2 - 3x + 4 = x^2 - 5x + 3

==> x^2 + 2x + 1 = 0

==> We will factor.

==> (x+1)^2 = 0

==> x= -1 ==> y= 9

Then the intersection point is (-1, 9)

The point ( -1, 9) is located into the second quadrant.

Then the curves meet in the second quadrant.