Question

Find the vertex of the quadratic equation: y = 2x^2 + 8x − 4.

Answer 1

your x value would be -b/2a
Solve for y with your x value

Answer 2

Because that makes sense..

Answer 3

I don't get it ..

Answer 4

b= coefficient of x= 8
a = coefficient of x^2 = 2

Answer 5

Make sense now?

Answer 6

ok stop

Answer 7

what is a coefficient?

Answer 8

ok 8x
The coefficient is the number that comes before it. Which is 8.
\[2x^2\] Your coefficient here would be 2.The number before it. Make sense?

Answer 9

... not really.

Answer 10

2x^2 + 8x - 4. I have to find the vertex.

Answer 11

So, what would the coefficients have to do with anything?

Answer 12

ok The number before a function or an unknown value x, a, b, n is called a coefficient.
If I have \[x^2 + 76x+87y+900n\]
My coefficients are 1, from x^2 76 from x 87 from y and 900 from n.

Answer 13

You're not paying attention are you?

Answer 14

I'm reading.

Answer 15

-b/2a
b and 2a ARE COEFFICIENTS FROM YOUR EQUATION.
The x value of your vector= -b/2a
Your y value is f(-b/2a)

Answer 16

Trying to get it, okay I get that part.

Answer 17

.. I don't get the vector part & f(-b/2a)

Answer 18

Is there a formula you could give me for this?

Answer 19

Your equation is in this form
\[ax^2+bx+c\]
a is the coefficient of x^2
b is the coefficient of x
and c is a constant.

Answer 20

Ok..

Answer 21

I gave you the formula in my FIRST comment
-b/2a = x value
then plug this value that you get into your equation to get the y value.
Your vertex is in this form (x,y)

Answer 22

why -b?

Answer 23

because that's the formula

Answer 24

so it'd be -8/2a?

Answer 25

a = -4?

Answer 26

a=2 coefficient of x^2
-4 is c

Answer 27

so your x value would be -8/2*2

Answer 28

so 8

Answer 29

\[-8/(2\times2)\]

Answer 30

-2

Answer 31

okay so the formula for this would be?
I'm going to write it down so I know how to do these.

Answer 32

yes that is one value of your vertex. The x value.
Now plug in -2 into your equation to find the y value and your answer should be in the form (x,y)

Answer 33

soo.. y = 2(-2)^2 + 8(-2) − 4.

Answer 34

yes..

Answer 35

-4^2 = 16
y = 16 + -16 - 4

Answer 36

y = -4

Answer 37

yes.

Answer 38

now back to the beginning

Answer 39

we have a problem

Answer 40

No its -12

Answer 41

my options to choose from are (−2, 20)

(−2, −12)

(2, 20)

(−2, −28)

Answer 42

how is it -12

Answer 43

2(4)+8(-2)-4= 8-16-4= -12

Answer 44

well. I don't get it.. once again..

Answer 45

Ok what don't you get?

Answer 46

The whole process.

Answer 47

ok do you remember how we got x?

Answer 48

No...

Answer 49

-b/2a

Answer 50

-b/2a= x

Answer 51

where b and a are coefficients.
Remember this.
\[ax^2 +bx +c\]
a is the number before x^2 (coefficient)
b is the number before x (coefficient)
and c is a constant. The number that's on it's own.