find the vertex and the x intercepts of y = x2 + 6x − 16??

- anonymous

find the vertex and the x intercepts of y = x2 + 6x − 16??

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- anonymous

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- anonymous

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- anonymous

|dw:1371220826248:dw| Then what?

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## More answers

- Jim766

-6/2 = ?

- anonymous

-3?

- phi

match a, b, c of
\[ a x^2 + b x + c \]
to your problem

- Jim766

right now sub it in to find the y part of the vertex
y = x2 + 6x − 16

- phi

if there is no number in front of a letter (as in x^2) it is understood to be 1

- Jim766

y = (-3)^2 + 6(-3) -16

- anonymous

so +9-18-16?

- Jim766

right, keep going...

- anonymous

-27=y?

- Jim766

close, but not what I got...

- anonymous

9-18=-11 right?

- Jim766

9-18 = -9

- anonymous

ohhhhhhhh right okay

- anonymous

so -25=y!

- Jim766

so that is the y part of the vertex and you found the x earlier
put them together to show your point (x, y)

- anonymous

(-3,-25)?

- Jim766

very nice!

- anonymous

Thank you!!! :DDD

- Jim766

now to find the x intercepts, you need to factor and solve
do you need help with that?

- anonymous

factor y = x2 + 6x − 16, right?

- Jim766

yeah, keep in mind the x intercept is where y = 0 so,
0 = x^2 + 6x -16

- Jim766

0 = (x )(x )

- anonymous

Okay so 0=(6-4)(x+4x^2)?

- Jim766

think if it this way we are looking for two things we can mult together to get
x^2 + 6x -16 I know that x * x = x^2
( x )(x ) now what 2 numbers can I mult to get -16
but also add them together and get +6

- anonymous

okay... uhh 4*-4 equals -16 but i dont think it can equal 6

- Jim766

good, keep going ...how else can you make -16 by multiplying?

- anonymous

8*2

- Jim766

right !

- anonymous

Is that it?

- Jim766

which one has to be negative to add them together and get +6
-8*2 or 8 * -2

- Jim766

which pair adds to + 6

- anonymous

it's (x+8)(x-2) i think!

- anonymous

oh wait

- anonymous

No its vice versa xD

- Jim766

good!
(x + 8)(x -2) = 0 now use zero prod property to solve each

- anonymous

How do you do that?

- Jim766

no, you were correct

- anonymous

Yay!

- Jim766

0 = x^2 + 6x -16
0 = (x +8)(x -2) zero prod property says that when two things are mult together
and equal zero, that one or both must equal zero, so that gives
us the right to do this
x + 8 = 0 or x -2 = 0 now solve each of these to find the x intercepts

- anonymous

so 8x=0 or -2x=0?

- Jim766

x + 8 = 0
-8 -8
x = -8 one x intercept is -8

- Jim766

x -2 = 0 solve this one

- anonymous

x-2=0
+2 +2
answer is +2!

- Jim766

right! so the x intercepts are { -8, 2} , or another way to write it x = -8 or x = -2

- Jim766

there are other ways to find the x intercepts of a quadratic... because factoring will not always work, but this is usually the first way they show you

- anonymous

Oh my god thank you so much :D you are super helpful!!

- Jim766

yw glad to help

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