Question

Determine whether the quadratic function show below has a minimum or maximum then determine the minimum or maximum value of the function
f(x) = 3x^2 - 18x + 29

Answer 1

Answer:

The quadratic has a minimum value.

The minimum value is at (3, 2).

Step-by-step explanation:

We are given the quadratic function:

$f(x)=3x^2-18x+29$

First, since the leading coefficient is positive, this quadratic function will be concave up.

Hence, we will have a minimum value.

The minimum or maximum value is the vertex of the quadratic. The vertex is given by:

$\displaystyle \Big(-\frac{b}{2a},f\Big(-\frac{b}{2a}\Big)\Big)$

In this case, a = 3, b = -18, and c = 29. Thus, the x-coordinate of the vertex is:

$\displaystyle x=-\frac{-18}{2(3)}=\frac{18}{6}=3$

And the minimum value is:

$f(3)=3(3)^2-18(3)+29=2$