A square is drawn such that one of its sides coincides with the line y = 7, and so that the endpoints of this side lie on the parabola y = 2x^2 + 6x + 4. What is the area of the square?
+128475 We need to find the width of the square........ we can do this as follows
2x^2 + 6x+ 4 = 7
2x^2 + 6x - 3 = 0
Using the q formula
x = [ -6 + sqrt ( 36 + 24) ] / [ 2 *2] = [ -6+ sqrt (60) ] / 4 = [ -6 + 2sqrt (15) ] / 4 = sqrt (15)/2 -3/2
The other root is -sqrt (15) / 2 - 3/2
These two points are where the parabola intersects the line y= 7
So....the width of the square = (-3/2 + sqrt (15)/2) - ( -3/2 - sqrt (15) / 2) = 2 sqrt (15) /2 = sqrt (15)
Area of the square = (sqrt (15)) ^2 = 15
