Suppose the g(x)=f(x+8)+4. Which statement best compare the graph of g(x) with the graph of f(x)?

1 answer:

8 0

In the translation of graph,
the image is
g(x)=f(x-h)+k
where
h=translation to the right
k=translation upwards.

For the given transformation,
g(x)=f(x-(-8))+4
we see that h=-8, k=+4
so we conclude that g(x) is a translation of f(x) 8 units to the left, and 4 units up.

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The roots of a quadratic equation ax2+bx+c=0 are 1+i 5 and 1−i 5 . Find possible values of a, b and c.

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Answer:

Step-by-step explanation:

If the roots are 1 + 5i and 1 - 5i, then you need the factors that result from those roots. They are (x - 1 + 5i) and (x - 1 - 5i). Now what you do with those is FOIL them out. Doing that gives you the following:

$x^2-x+5ix-x+1-5i-5ix+5i-25i^2$ (what a mess, huh?)

The good thing is that several of those terms cancel each other out. +5ix cancels out the -5ix; -5i cancels out the 5i; and the 2 -x terms combine to -2x. That leaves you with:

$x^2-2x-25i^2$

Obviously you're in the section in math that deals with complex (imaginary) numbers so you should know that i-squared is equal to -1. Making that replacement:

$x^2-2x+25$