2 years ago

What are the features of the quadratic function f(×) =×2 +10×+21?

Mathematics

1 answer:

laiz [17]2 years ago

8 0

A is the correct answer

Vertex = (-5,-4), y-intercept = (0,21), x-intercepts = (-7,0) and (-3,0), axis of

symmetry is x = -5

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Establish for which constants c the following function is a density.

Valentin [98]

By "density" I assume you mean "probability density function". For this to be the case for $f(x)$ , we require

$\displaystyle\int_{-\infty}^\infty f(x)\,\mathrm dx=1$

Since

$f(x)=\begin{cases}cx^{1/2}&\text{for }0$

you have

$\displaystyle\int_{-\infty}^\infty f(x)\,\mathrm dx=\int_0^2cx^{1/2}\,\mathrm dx=\dfrac{2c}3x^{3/2}\bigg|_{x=0}^{x=2}=\dfrac{2^{5/2}c}3=1$

which means

$c=\dfrac3{2^{5/2}}=\dfrac3{4\sqrt2}$