Which direction would the graph of y=3|x|-8 open

Mathematics

2 answers:

ss7ja [257]3 years ago

8 0

The graph would open at the down at the bottom

irina1246 [14]3 years ago

6 0

Answer:

The graph of given function open upward.

Step-by-step explanation:

The given equation is

$y=3|x|-8$ ....(1)

The general form of an absolute function is

$f(x)=a|x|+b$ .....(2)

If a>0, then the graph of function open up and if a<0, then the graph of function open down.

On comparing (1) and (2), we get

$a=3,b=-8$

Since a=3>0, therefore the graph of given function open upward.

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The expression $\frac{m^{2}-16\cdot n^{2}}{\frac{3\cdot m + 12\cdot n}{m\cdot n} }$ is equal to $\frac{m^{2}\cdot n}{3} -\frac{4\cdot m\cdot n^{2}}{3}$ .

<h3>How to simplify a composite algebraic expression</h3>

In this question we must use properties of <em>real</em> algebra to simplify a given expression as most as possible. We proceed to show each step with respective reason.

$\frac{m^{2}-16\cdot n^{2}}{\frac{3\cdot m + 12\cdot n}{m\cdot n} }$ Given
$\frac{m\cdot n \cdot (m^{2}-16\cdot n^{2})}{3\cdot m + 12\cdot n}$ $\frac{\frac{a}{b} }{\frac{c}{d} } = \frac{a\cdot d}{c\cdot b}$
$\frac{m\cdot n \cdot (m-4\cdot n)\cdot (m+4\cdot n)}{3\cdot (m+4\cdot n)}$ Distributive property/ $a^{2}-b^{2} = (a +b)\cdot (a-b)$
$\frac{m\cdot n \cdot (m-4\cdot n)}{3}$ Existence of the multiplicative inverse/Modulative property
$\frac{m^{2}\cdot n}{3} -\frac{4\cdot m\cdot n^{2}}{3}$ Distributive property/ $x^a\cdot x^{b} = x^{a+b}$ /Result