Question

Identify which quadratic functions have a maximum value and which have a minimum value. what is that value?

a) y = -35 (x + 100)^2 - 1200
b) R(x) = 1/2(x - 37)^2 + 37

Answer 1

A quadratic function has a maximum value if the coefficient of the squared term is negative and a minimum value if it is positive. Function (a) has a maximum value of -1200, and function (b) has a minimum value of 37.

Step-by-step explanation:

To identify whether a quadratic function has a maximum or minimum value, we look at the coefficient of the x^2 term. If it is positive, the function has a minimum value; if negative, a maximum value. The value can be found at the vertex of the parabola.

• For y = -35(x + 100)^2 - 1200, the coefficient of (x + 100)^2 is -35, which is negative, indicating that this function has a maximum value. The maximum value is the y-coordinate of the vertex, which is -1200.
• For R(x) = 1/2(x - 37)^2 + 37, the coefficient of (x - 37)^2 is 1/2, which is positive, meaning this function has a minimum value. The minimum value is the y-coordinate of the vertex, which is 37.