Step-by-step explanation:
they're is a neat little trick.
but first of all, "roots" means the 0 solutions of the equation. like
ax² + bx + c = 0
there are 2 solutions for x to make the whole expression equal 0.
these are the "roots".
now to the little trick :
when is a multiplication resulting in 0 ?
when at least one of the factors is 0.
and any quadratic expression can be written as multiplication of 2 factors. like
c(x - a)(x - b) = cx² - cax - cbx + cab
what are the "roots" or 0 points ?
either
c = 0
x - a = 0 | x = a
x - b = 0 | x = b
the leading coefficient = 3.
that means nothing else than c = 3.
root = 1 means (x - 1) is one factor.
root = -5 means (x + 5) is the other factor.
so, we have
3(x - 1)(x + 5) = 3x² + 12x - 15
and the equation is
3x² + 12x - 15 = 0
or
3x² + 12x = 15
Answer:
60
Step-by-step explanation:
Set up a ratio problem
15/25 = 36/x
15x = 900
x = 60
Answer:
4(5+8)
Step-by-step explanation:
The GCF of 20 and 32 is 4. Then you divide 20 and 34 by 4.
Answer:
g(x)=3(x+3)^2-8
Step-by-step explanation:
You can solve by using these acronyms.
H. orozontal.
I. nside.
O. pposite.
Meaning that a horozontal translation would be written inside the parenthesis and the poopsite sigh you would usually (Ex. Left is usually negitave but in this case it is positive).
The other acronym is,
V. erticle.
O. utside.
S. ame.
Meaning for a vrerticle translation the number would go on the outside of the parenthesis and tha sign would be normal (Ex. Negitave would be left and positive would be right).
For this one use H.I.O sinse you are moving on a horozontal plain. You are only working with the (x-2) nothing else matters.
Since you are moving left the number will move up 3 hence the O.
<h2><u>This transformation leaves you with g(x)=3(x+3)^2-8</u></h2>
