Quadratic Functions

[willd]

A quadratic function has a definite maximum or minimum point
(its vertex) that other polynomials may not have. This makes it a good
candidate for use in application problems that may require finding a
maximum or minimum quantity. If A(x) = -6x2 + 2x + 3 is used
to describe a situation involving Area, or Altitude, or Age. How would
you go about using the function and its graph to determine the maximum
area, altitude or age?

 

[soroban]

Hello, willd!

You already know so much about the parabola, you should know the answer . . .

For a parabola, y = ax² + bx + c, its vertex is at: . x = -b/2a

Your function, A(x) .= .-6x^2 +2x + 3, is a down-opening parabola.
. . Hence, its vertex is a maximum value for the function.

We have: a = -6, b = 2, c = 3. .Hence, x = -2/[2(-6)] = 1/6

And the maximum value is: .A(1/6) .= .-6(1/6)² + 2(1/6) + 3 .= .19/6