Can any one help me please

Mathematics

1 answer:

ELEN [110]3 years ago

4 0

The one that looks like a u is a quadratic function

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yKpoI14uk [10]

A binomial squared is written like

$x^2+2ax+a^2$

So, we have $2a=6 \iff a=3$

So, we want to complete the square $(x+3)^2 = x^2+6x+9$

We can add and subtract 9 to write

$x^2+6x = x^2+6x+(9-9) = (x^2+6x+9)-9 = (x+3)^2-9$

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3 years ago

Which of the following graphs of exponential functions corresponds to a geometric sequence with a first term of 4 and a ratio of

ser-zykov [4K]

Answer: graph E.

A geometric sequence can be written as:

$a_{n} = a_{1} \cdot r^{(n - 1)}$

where:

a₁ = first term = 4

r = ratio = 0.5

Substituting the numbers, we have:

$a_{n} = 4 \cdot (\frac{1}{2})^{n-1}$

or else

$f(x) = 4 \cdot (\frac{1}{2})^{x - 1}$

This is an exponential function with base less than 1. Therefore, we can exclude graph C (which depicts a linear function), and graphs A and D (which depict an exponential function with base greater than 1).

In order to choose between graph B and E, let's evaluate the function in two different points:

$f(1) = 4 \cdot (\frac{1}{2})^{1 - 1} = 4$