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never [62]
3 years ago
14

The image shows a geometric representation of the function f(x)=x^2-2x-6 written in standard form. What is the function written

in vertex form?
Mathematics
2 answers:
Degger [83]3 years ago
9 0
Y=(x-1)^2-7 This is this function in vertex form
Dominik [7]3 years ago
9 0

Answer:

y=(x-1)^2-7

Step-by-step explanation:

Given : Equation = f(x)=x^2-2x-6

To write in vertex form

Vertex form =  y = a(x - h)^2+ k

The given equation is in standard form y=x^2-2x-6

to convert into vertex form we can use completing the square,

step 1 : y=x^2-2x-6

step 2 : y+6=x^2-2x

step 3 : y+6+1=x^2-2x+1

step 4 : y+7=(x-1)^2

step 5 : y=(x-1)^2-7

It is a vertex form where a=1, h=1 , k=-7


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Use a matrix to solve the system:
Romashka-Z-Leto [24]

Answer:

(2.83 , 1 , 4)

Step-by-step explanation:

2x+2y-z=4\\4x-2y-2z=2\\3x+3y-4z=-4\\

Rewrite these equations in matrix form

\left[\begin{array}{ccc}2&2&-1\\4&-2&-2\\3&3&-4\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right]=\left[\begin{array}{ccc}4\\2\\-4\end{array}\right] \\

we can write it like this,

AX=B\\X=A^{-1}B

so to solve it we need to take the inverse of the 3 x 3 matrix A then multiply it by B.

We get the inverse of matrix A,

A^{-1}=\left[\begin{array}{ccc}7/15&1/6&-1/5\\1/3&-1/6&0\\3/5&0&-2/5\end{array}\right]  \\

now multiply the matrix with B

X=A^{-1}B\\\\\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}7/15&1/6&-1/5\\1/3&-1/6&0\\3/5&0&-2/5\end{array}\right]\left[\begin{array}{ccc}4\\2\\-4\end{array}\right] \\\\\\\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}2.83\\1\\4\end{array}\right] \\

4 0
3 years ago
A snake bar sold 12 1/2 gallons of milk at 35 cents a pint. How much did the snack bar receive for the milk
stepladder [879]

9514 1404 393

Answer:

  $35.00

Step-by-step explanation:

The number of pints sold is ...

  (12.5 gal)×(8 pt/gal) = 100 pt

Then the total amount received for the milk is ...

  (100 pt)($0.35/pt) = $35.00

8 0
2 years ago
Can someone pleaseeee help and if you’re correct i’ll give brainliest
matrenka [14]
The answer is the
The shape has 6 equal Square face
Because each side had 6

That on of the answer the next the shape has 6 vertices

Also the shape is soild
4 0
3 years ago
Solve the equation by using the Properties of Equality.<br> 9x – 3 = 42
Naya [18.7K]

Step-by-step explanation:

9x-3=42

9x=42+3

9x=45

9x/9=45/9

x=5

3 0
3 years ago
(b) In a lab, a substance was heated by 6 °C each hour for 24 hours. What was the total change
WINSTONCH [101]

Answer:

144

Step-by-step explanation:

3 0
2 years ago
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