Point p(a, b) is in the first quadrant on the graph of the line x+y=4. a triangular region is shown on the diagram. what is the maximum area of the triangular region?

4

Step-by-step explanation:

Area of Triangular region (A) = a x b

b = 4 - a  (for point (a,b) and x + y = 4)

A = a x (4 - a) = - a² + 4a = -(a² - 4a + 4) + 4 = - (a - 2)² + 4

in the formula of parabola y = a(x - h)² + k, a= -1  the graph is pointed down where h=2 and k=4

The vertex is (2, 4)

The maximum area of triangular region is 4

step-by-step explanation:

3024 rhe base is what up in worry about

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.