The area of the triangle 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 upward.

a = 4

Step-by-step explanation: Area of a triangle is calculated as: .

The triangle formed by the parabola has base (b) equal to the distance between the points where the graph touches x-axis and height (h) is the point where graph touches the y-axis.

The points on the x-axis are the roots of the quadratic equation:

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

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

x - 3 = 0

x = 3

or

x + 2 = 0

x = -2

So, base is the distance between (-2,0) and (3,0).

Since they are in the same coordinate, distance will be:

b = 3 - (-2)

b = 5

Area of the triangle is 10. So constant a is

5a = 10.2

a = 4

The constant a of the function y = a(x-3)(x+2) is 4.

the answer to the expression is 83

6 hours 48 min

step-by-step explanation:

68÷5=13.6

13.6×30=408min=6 hours 48 min.

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