Question

Find all the points if any where y-4x=12 intersects 2-y=2(x+2)^2

A) there are no points of intersection

B) (-3,0)

C) (3,0)

D) (-3,0) and (3,0)

Answer 1

B

Explanation:

given the 2 equations

y - 4x = 12 → (1)

2 - y = 2(x + 2)² → (2)

rearrange (1) expressing y in terms of x

y = 12 + 4x

Simplify (2) by expanding factor and substituting y = 12 + 4x

2 - (12 + 4x) = 2(x² + 4x + 4)

2 - 12 - 4x = 2x² + 8x + 8

- 10 - 4x = 2x² + 8x + 8 ← rearrange into standard form

add 10 + 4x to both sides

2x² + 12x + 18 = 0 ← in standard form

divide through by 2

x² + 6x + 9 = 0

(x + 3)(x + 3) = 0 ⇒ (x + 3)² = 0 ⇒ x = - 3

Point of intersection = (- 3, 0 ) → B