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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?

Point pab is in the first quadrant on the graph of the line xy4 A triangular region is shown on the diagram What is the maximum area of the triangular region class=

Respuesta :

Answer:

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

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