Subtract -6 from both sides
3x^2 + 17x + 4 - (-6) = -6 - (-6)
3x^2 + 17x + 10 = 0

factor left side of equation
(3x+2)(x+5)=0

set factors to 0
x = -2/3 OR x = -5

I would go with -5

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4 years ago

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As shown at the right, rectangle abcd has vertices c and d on the. V-axis and vertices a and b on the part of the parabola y — 9

Sergio039 [100]

a) The <em>perimeter</em> function of the rectangle is $p = 18\cdot x -2\cdot x^{3}$ .

b) The domain of the <em>perimeter </em>function is $x \in [-3, 3]$ .

<h3>How to analysis the perimeter formula of a rectangle inside a parabola</h3>

a) The perimeter of a rectangle ( $p$ ) is the sum of the lengths of its four sides:

$p = AB\cdot AC$ (1)

If we know that $AB = 2\cdot x$ and $AC = 9-x^{2}$ , then the perimeter of the rectangle is represented by the following formula:

$p = 2\cdot x \cdot (9-x^{2})$

$p = 18\cdot x -2\cdot x^{3}$

The <em>perimeter</em> function of the rectangle is $p = 18\cdot x -2\cdot x^{3}$ . $\blacksquare$

b) The domain of the function is the set of values of $x$ associated to the function. After a quick inspection, we find that the domain of the <em>perimeter </em>function is $x \in [-3, 3]$ . $\blacksquare$

<h3>Remark</h3>

The statement is incomplete and poorly formatted. The correct form is described below:

<em>As shown at the right, rectangle ABCD has vertices C and D on the x-axis and vertices A and B on the part of the parabola </em> $y = 9-x^{2}$ <em> that is above the x-axis. a) Express the perimeter </em> $p$ <em> of the rectangle as a function of the x-coordinate of A. b) What is the domain of the perimeter function?</em>