Question

Answer the questions below about the quadratic function.

g(x) = 3x² – 30x + 74
Does the function have a minimum or maximum value?
Where does the minimum or maximum value occur?
What is the function's minimum or maximum value?

Answer 1

Explanation:

Answer 2

Minimum.

(5, -1).

-1.

Explanation:

Minimum value as the coefficient of x^2 is positive.

Convert to vertex form to find the minimum point:

3x^2 - 30x + 74

= 3(x^2 - 10x) + 74

= 3[(x - 5)^2 - 25 ] + 74

= 3(x - 5)^2 - 75 + 74

= 3(x - 5)^2 - 1.

This vertex form shows that the minimum is at the point (5, -1).

The value of the minimum is -1.