In how many distinct points does the graph of: y = 3/2x^ 2 - 5x - 1/4y=32x2−5x−14 intersect e graph y = -1/2x ^2 + 2x - 7 y=−12x2+2x−7 in the viewing rectangle [-10,10] by [-15,5]?

1 Answer
Shwetank Mauria
Oct 4, 2016

The two graphs do not intersect each other.

Explanation:

As we have two intersecting graphs

y=3/2x^2-5x-1/4y=32x2−5x−14 and

y=-1/2x^2+2x-7y=−12x2+2x−7

at intersecting point we will have 3/2x^2-5x-1/4=-1/2x^2+2x-732x2−5x−14=−12x2+2x−7

or 3/2x^2+1/2x^2-5x-2x-1/4+7=032x2+12x2−5x−2x−14+7=0

or 2x^2-7x+6 3/4=02x2−7x+634=0

or 8x^2-28x+27=08x2−28x+27=0

As the discriminant b^2-4ac=(-7)^2-4xx8xx27=49-864=-815b2−4ac=(−7)2−4×8×27=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]}

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