4 years ago

Convert this quadratic function to vertex form.

1 answer:

3 0

Y=x² +14x +48
y-48 = x² +14x
y-48+7² = x² +2*7*x +7²
y-48+49 = (x+7)²
y+1= (x+7)²
y=(x+7)² - 1

Vertex of the function is (-7,-1). Minimum value of this function is a vertex value , because parabola directed up.

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1) The rational function shown could be used to the number of arrests, f(x), per 100,000 drivers, for driving under the influenc

swat32

The age that has the maximum number of arrest is 25 years

<h3>The trend on the graph</h3>

The equation of the function is given as:

$f\left(x\right)\ =\ \frac{27725\left(x\ -\ 14\right)}{x^{2\ }+\ 9}-5x$

See attachment for the graph of the function.

The end behavior of the graph is

$\mathrm{as}\:x\to \:+\infty \:,\:f\left(x\right)\to \:-\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:f\left(x\right)\to \:+\infty \:$

This means that:

As the age of the driver increases, arrested drivers decreases and as the age of the driver decreases, arrested drivers increases

<h3>The age that has the maximum arrest</h3>

From the graph, the maximum is:

Maximum = (25.388, 356.166)

Remove the y values

Maximum = 25.388

Approximate

Maximum = 25

Hence, the age that has the maximum arrest is 25