The area of a triangle is formed by points of intersection of parabola y=a(x-3)(x+2) with the coordinate axes is 10. Find A if it is known that parabola opens upwards

Question

asked May 21, 2022 4.4k views

2 Answers

Lucas Romier · Answer 1 · 2022-05-21T19:04:02+0000

Answer:

a=2/3

Explanation:

1. y=a(x-x1)(x-x2) is a formula for a parabola, x1 and x2 being points where y=0 so in the equation y=a(x-3)(x+2), you know

x1=3, x2=-2

2. Find distance between 3 and -2, which is 5

3. bh/2=A --> 5h/2=10 --> h=4 (h is height)

4. when x=0, y=-6a, y=a(0-3)(0+2)

5. because parabola opens upward, the point of the vertex must be (_, -4)

6. -6a= -4

a=2/3