# 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]?

Oct 4, 2016

The two graphs do not intersect each other.

#### Explanation:

As we have two intersecting graphs

$y = \frac{3}{2} {x}^{2} - 5 x - \frac{1}{4}$ and

$y = - \frac{1}{2} {x}^{2} + 2 x - 7$

at intersecting point we will have $\frac{3}{2} {x}^{2} - 5 x - \frac{1}{4} = - \frac{1}{2} {x}^{2} + 2 x - 7$

or $\frac{3}{2} {x}^{2} + \frac{1}{2} {x}^{2} - 5 x - 2 x - \frac{1}{4} + 7 = 0$

or $2 {x}^{2} - 7 x + 6 \frac{3}{4} = 0$

or $8 {x}^{2} - 28 x + 27 = 0$

As the discriminant ${b}^{2} - 4 a c = {\left(- 7\right)}^{2} - 4 \times 8 \times 27 = 49 - 864 = - 815$ 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]}