A). |x| = |-x|
This is always true.
The definition of 'absolute' value is 'size of the number without its sign'.
That's what this expression says.
b). |x| = -|x|
This is never true, because an absolute value is never negative.
This one would true if x=0 . So maybe some people might say
it's sometimes true, but that doesn't feel right to me. I say never.
c). |-x| = -|x|
This looks to me like exactly the same situation as (b),
and I would say all the same things about it.
-43
-44
-45.
-43 + -45 is -88
We have that
f(x) = –4x²<span> + 24x + 13
</span>
we know that
The vertex form for a parabola that opens up or down is:
f(x) = a(x - h)^2 + k
in the given equation, <span>a=-4</span><span>, therefore we add zero to the original equation in the form of </span><span>4h</span>²<span>−4h</span>²
f(x) = –4x² + 24x + 4h²−4h² +13
<span>Factor 4 out of the first 3 terms and group them
</span>f(x) = –4*(x² -6x +h²) +4h² +13
<span>We can find the value of h by setting the middle term equal to -2hx
</span>−2hx=−6x
<span>h=3</span><span> and </span><span>4h</span>²<span>=<span>36
</span></span>f(x) = –4*(x² -6x +9) +36 +13
we know that the term (x² -6x +9) is equals to------> (x-3)²
so
f(x) = –4*(x-3)² +49
the answer isf(x) = –4*(x-3)² +49
