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the fastest way to solve this problem on
the ged
when you have an x squared and an equal sign
sign
is to use the calculator
because there's a button on there called table
table
and we can type in the left side of this
equation here
so we'll start off with x squared
x is right there next to four
squared is right above it
then minus three x
x
minus four
from there you're just going to keep
hitting enter until you get to a table
we want to find out when the whole thing
is six
or when the y value is six
but if we just sneak down a little bit
when x is negative two
the whole thing is six
so therefore x is negative two is one of
our answers
now none of the other ones have a
negative two so the other answer should
just be positive five
all right well let's just double check that
that
and that does check out when x is five
the whole thing is six just like we want
so it's got to be b because those are
both of our answers there
when you have those squigglies it just
means multiple answers are correct
okay but what was going on because that
might have seemed like a bunch of black
magic there
well let's clear let's go to the home screen
screen
when you have this equation here we're
really just changing both of these x's
to the same number
so let's pretend we change both of those
x's 5 there
5 there
let's do it
so it's going to be 5 and that one's squared
squared
then minus
when you have a number and a letter next
to each other they're just multiplied
so we'll do three times same x value of five
five
end it with a minus four
and that gets us six
so that's why that value worked
and if we plugged in negative 2 for that
x and that x
that would also get us positive 6.
so that's what's really going on behind
the scenes
the amazing thing is the table button
just went ahead and plugged in all of
these all at once so saved us a lot of
time there
okay here's another example if you want
and let's jump into it so fastest way
when we see an x squared and an equal sign
sign
use that table
we'll clear
and let's do it
x squared minus two x
minus three
enter five times
but this time we're looking when the
solution is zero or the y value is zero
but lucky for us right away we notice oh
when x is three the whole thing is zero so
so
that one must be an answer
but once again
none of the other ones have positive
three so it looks like x is negative one
is the other answer
we'll go up to get to the negatives there
there
and sure enough x is negative one that
also works
so a those are both of our answers
okay so we could solve these all day but
what's the application here
when you have an x squared and you graph
it it's actually a smiley face
and it could represent the height of a
skateboarder on a half pipe over time
or if you have a negative x squared
that's just a frown
so that could represent the height of a
football or soccer ball being kicked
reaches a peak
comes back down hits the ground
but notice we set ours equal to zero
that's the same thing as finding out
when the height is zero
or how long it took before it hit the ground
ground
our answers are both how long it took
but negative time doesn't make sense so
we'll ignore that one
but it took three seconds after we
kicked it four the height to be zero and
hit the ground
so that's how you could use those guys there
okay here's another one
even if there's a number in front of x
squared no worries same thing
so let's do it
table clear 3
3
x squared
minus 4x enter
enter
and we're on the hunt for when y is 20.
okay let's scroll down
but no we're not seeing it there let's
go back up
and there we go
when x is negative 2 the whole thing is
20. so answer there should be d
now we could always double check it
because we could plug in negative 2 for
x there
negative 2 for x there and we could type
that in
when you replace a letter with a number
then just put it in parentheses
and then that'll work correctly
that all should give us 20.
20.
and then there's one last example here
okay this one looks a little extra but
no worries still the same process here
the only issue is when we get to the
fractions but we'll address that when we
get there
okay let's start it off
so table clear this one has a 3x squared
plus 13x
minus 10
enter five times
the only issue with the table is it only
tells you whole numbers
so we can only check whether five and
negative five work
but that's fine let's check positive
five let's scroll down
okay but that gets us 130.
we want it to be zero so it's definitely
not that one
but let's go ahead and check negative
five here let's scroll up to get to the negatives
negatives
and there we go that does work
x is negative five the whole thing is zero
zero
so that one's good
now when we're trying to check fractions
we could still do table
type it in just like we have but then
hit enter once
because we're going to scroll down
switch it from auto to ask
this allows us to plug in any x value we want
want
two thirds for instance okay so we'll
hit that
and let's do it so we'll hit 2
fraction 3
that'll plug in x is 2 3 for that x and
that x and
and
that does surprisingly give us zero
so that answer works
but we already have our two answers so
we know what those are
okay but let's just check negative
two-thirds just to make sure that that
doesn't work
and no it gives us some negative so no good
good
so let's get rid of that
okay so x is negative five was one answer
answer
positive two-thirds the other answer
and that's it
you'll be able to solve any quadratic or
x-squared problem on the ged using this method
method
you got these let me know what questions
you have but good luck
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