Question

At which points do the functions
y
−
2
x
=
x
2
−
3
and
2
y
−
x
−
14
=
0
intersect?


(
−
5
2
,
33
4
)
and
(
4
,
5
)


(
−
4
,
33
4
)
and
(
5
2
,
5
)


(
−
4
,
5
)
and
(
5
2
,
33
4
)


(
5
,
−
4
)
and
(
33
4
,
5
2
)

Answer 1

Solve y = x^2 + 2x - 3 and y = (x+14)/2. Set equal:

x^2 + 2x - 3 = (x+14)/2
=> 2x^2 + 4x - 6 = x + 14
=> 2x^2 + 3x - 20 = 0

Discriminant = 3^2 - 4·2·(-20) = 169, so x = (-3 ± 13)/4 = 5/2 or -4.
y(5/2) = (5/2 + 14)/2 = 33/4, y(-4) = (-4 + 14)/2 = 5.

Thus the intersection points are (-4, 5) and (5/2, 33/4) — the third choice.