Question

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]?

Answer 1

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]}