The area of triangle formed by points of intersection of parabola y=a(x−1)(x−4) with the coordinate axes is 3. Find a if it is k

Question

Nikolay [14]

3 years ago

11

The area of triangle formed by points of intersection of parabola y=a(x−1)(x−4) with the coordinate axes is 3. Find a if it is k

nown that parabola opens downward.

Mathematics

1 answer:

suter [353] · Answer 1 · 2021-12-22T15:03:42+03:00

Answer:

a = -1/2

Step-by-step explanation:

In order for the triangle with a base of 4-1 = 3 units to have an area of 3 square units, the height of it must be 2. Since the parabola opens downward, the y-intercept of the equation must be -2. Filling in known values for that point, we have ...

-2 = a(0 -1)(0 -4)

-2 = 4a . . . . . . . . . simplify

-2/4 = a = -1/2