The parabolas y = -3x2 + 10x - 6 and y = -3x2 - 17x + 2 intersect at _____?

Question

A.the line y = 27x - 8.

B. x=the square root of 2 over 3 and xthe -square root of 2 over 3.

C. x=8/27.

D. they do not intersect.

Answer 1

two curves intersect in a point, so

A is out

solving the equation

-3x^2 + 10x - 6 = -3x^2 - 17x + 2
yields x = 8/27

Answer 2

- 3 x ^ 2 + 10 x - 6 = - 3 x ^ 2 - 17 x + 2

Add 3 x ^ 2 + 17 x - 2 to both sides.

- 3 x ^ 2 + 3 x ^ 2 + 10 x + 17 x - 6 - 2 = - 3 x ^ 2 + 3 x ^ 2 - 17 x + 17 x + 2 - 2

27 x - 8 = 0

Add 8 to both sides.

27 x - 8 + 8 = 0 + 8

27 x = 8 Divide both sides by 27

x = 8 / 27

when x = 8 / 27

- 3 x ^ 2 + 10 x - 6 = - 3 * ( 8 / 27 ) ^ 2 + 10 * 8 / 27 -6 =

- 3 * 64 / 729 + 10 * 8 / 27 - 6 =

- 192 / 729 + 80 / 27 - 6 =

- 192 / 729 + 27 * 80 / 729 + 6 * 729 / 729 =

- 192 / 729 + 2160 / 729 - 4374 / 729 =
- 2406 / 729 = - 3 * 802 / ( 3 * 243 ) =

- 802 / 243

Intersection point ( 8 / 27 , - 802 / 243 )

Answer 3

Thank youu! (: