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Which of the following points is a location where the function f(x) = -2x² + 12x + 54 crosses the horizontal axis?
TSI Math: Finding Solutions to an Equation through Factoring 6 Views
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Description:
Which of the following are the solutions to the equation -4x² + 2x + 6 = 0?
- Test Prep / TSI
- Intermediate Algebra and Functions / Quadratic and Other Polynomial Expressions, Equations, and Functions
- TSI / TSI Math
- TSI / TSI Mathematics
- TSI Mathematics / Intermediate Algebra and Functions
- Intermediate Algebra and Functions / Quadratic and Other Polynomial Expressions, Equations, and Functions
- Test Prep / TSI
- TSI Math / Intermediate Algebra and Functions
Transcript
- 00:02
Okay sy mass members here we go More expressions equations
- 00:05
functions Which of the following are the solutions to the
- 00:07
equation and negative for x squared plus two x plus
- 00:10
six Oh poor negative for expert plus two x plus
- 00:18
six equals zero Looks a little bloated Helped the equation
Full Transcript
- 00:21
Shed some weight here and let's factor out some well
- 00:24
common factors It's More trouble than it's worth factor with
- 00:27
a negative leading coefficient right Well when negative for x
- 00:30
squared plus two x plus six jumps on the equation
- 00:33
Treadmill The first factor it sweats out is a negative
- 00:36
one there So pull the negative out of each term
- 00:38
by swapping the signs and then that's how we do
- 00:41
it Okay well each coefficient is even so too is
- 00:44
another common factor Let's Move it on out front as
- 00:47
well So we got negative two times This whole thing
- 00:49
in here The extra weight is still hovering around by
- 00:51
both sides of the equation by negative too To shed
- 00:54
it for good If only burning off the dozen donuts
- 00:56
alina here may not have eaten yesterday Were this easy
- 00:59
Don't ask Okay so here we go We got to
- 01:01
x squared minus x minus three is zero Well it
- 01:05
feels good to have a lighter equation to factor and
- 01:07
solved now because what leading coefficient of polynomial is to
- 01:11
the factor to x squared minus Acts minus 3 Well
- 01:16
we'll need to do ah little guessing and checking the
- 01:18
first step of guests and check involves listing all the
- 01:22
factors of the leading term Well in this case we
- 01:25
can guess that the first two terms are ex and
- 01:28
two x The second step is to find the factors
- 01:31
of the constant negative three Well the factors will either
- 01:34
be negative three and one or negative One and three
- 01:38
Right Well now it's Time to do some guessing at
- 01:41
fill in two of the possible factors in the second
- 01:44
term of each of your parentheses There right there Since
- 01:47
we know the outside terms will be multiplied together Well
- 01:49
it's probably a better idea to put a three on
- 01:51
the inside term since we know we're aiming for a
- 01:54
middle term of negative one acts right there Multiplying this
- 01:58
out using foil Get following The first two terms will
- 02:01
multiply two to x squared No surprise there The two
- 02:05
outside terms multiply to be positive Two Acts while the
- 02:08
2 inside terms will apply to a negative three x
- 02:11
and our final term yes is negative three Well again
- 02:14
no Surprise on that last one right there Yeah combined
- 02:17
like terms to see that we've actually hit the nail
- 02:20
on the head out with our first guests Well now
- 02:23
that the equations factored either to x minus three or
- 02:26
x plus one must equal zero for the entire equation
- 02:30
equals zero so we just set Each factor equals zero
- 02:33
and solve here so to x minus three zero two
- 02:35
exes three exes three halves or x plus one a
- 02:39
zero and x is negative one Well after only a
- 02:41
few minutes of solving the equation is cleansed of the
- 02:44
solutions so x equals three halves and x equals negative
- 02:48
one So that's a that's Our answer And we're going
- 02:52
to go look lovingly at the new crispy cream discount 00:02:55.02 --> [endTime] coupon ad Hello
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