In how many distinct points does the graph of: #y = 3/2x^ 2 - 5x - 1/4# intersect e graph #y = -1/2x ^2 + 2x - 7 # in the viewing rectangle [-10,10] by [-15,5]?

1 Answer
Oct 4, 2016

Answer:

The two graphs do not intersect each other.

Explanation:

As we have two intersecting graphs

#y=3/2x^2-5x-1/4# and

#y=-1/2x^2+2x-7#

at intersecting point we will have #3/2x^2-5x-1/4=-1/2x^2+2x-7#

or #3/2x^2+1/2x^2-5x-2x-1/4+7=0#

or #2x^2-7x+6 3/4=0#

or #8x^2-28x+27=0#

As the discriminant #b^2-4ac=(-7)^2-4xx8xx27=49-864=-815# is negative, we do not have any roots (or real solutions) to above equation.

Hence the two graphs do not intersect each other.

graph{(y-3/2x^2+5x+1/4)(y+1/2x^2-2x+7)=0 [-10, 10, -15, 5]}