Question

partially correct
your answer is incorrect.

• (b): your answer is incorrect.
• (c): your answer is incorrect.

answer the questions below about the quadratic function.
$g(x) = 3x^2 + 24x + 47$
your answer
(a) does the function have a minimum or maximum value?
minimum maximum
(b) where does the minimum or maximum value occur?
x = -4, -1
(c) what is the functions minimum or maximum value?
-4

Explanation:

Step1: Analyze the quadratic function form

For a quadratic function \( g(x) = ax^2 + bx + c \), the coefficient \( a \) determines if it has a minimum or maximum. Here, \( a = 3>0 \), so the parabola opens upward, meaning it has a minimum.

Step2: Find the x - coordinate of the vertex (where min/max occurs)

The formula for the x - coordinate of the vertex of a quadratic function \( g(x)=ax^{2}+bx + c \) is \( x=-\frac{b}{2a} \). For \( g(x)=3x^{2}+24x + 47 \), \( a = 3 \) and \( b = 24 \). Substitute these values into the formula: \( x=-\frac{24}{2\times3}=-\frac{24}{6}=-4 \).

Step3: Find the minimum value of the function

We can substitute \( x = - 4 \) into the function \( g(x)=3x^{2}+24x + 47 \).

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Answer:

(b) The minimum value occurs at \( x=-4 \)
(c) The minimum value of the function is \( - 1 \)