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stiks02 [169]
2 years ago
5

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
Mathematics
1 answer:
REY [17]2 years ago
3 0

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

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