Respuesta :
Answer:
The value of a will be [tex]a=-\frac{1}{2}[/tex]
Step-by-step explanation:
Start by graphing the parabola and the three points of the triangle. These points are at intersections of y=a(x-1)(x-4) and the axes
so the y = 0 points are (1,0) and (4,0).
The x = 0 intersection is when y=a(-1)(-4) or (0,4a)
The base and height of this triangle are
The base would be the distance between the y=0 intersections and the height would be the y value of the other vertex.
Hence, base=3 units and height = 4a units. Thus, area can be calculated as
[tex]A = \frac{1}{2}\times b\times h =\frac{1}{2}\times 3\times 4a = 3[/tex]
[tex]a=\frac{1}{2}[/tex]
∵ the parabola opens downward therefore a will be negative.
hence, [tex]a=-\frac{1}{2}[/tex]
