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Harman [31]
2 years ago
11

Write the quadratic function in vertex form. Then identify the vertex.

Mathematics
1 answer:
ddd [48]2 years ago
7 0

Answer:

Step-by-step explanation:

To put the equation into vertex form, we need to complete the square

g(x) = (x^2 - 4x + ...) - 1\\g(x) = (x^2-4x+(\frac{4}{2})^2 ) - 1 - (\frac{4}{2})^2 \\g(x) = (x-2)^2 - 5\\

This is in the form

y = a(x-h)^2 + k\\(h, k)

So, the vertex is (2, -5)

and g(x) = (x-2)^2-5

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A function f(x)f(x) is graphed on the coordinate plane.
Effectus [21]

<u>Answer</u>

-4x - 2


<u>Explanation</u>

To get the function needed, first calculate the slope of the graph.

slope = (change in y) / (change in x)

          = (2 - -2)/(-1 - 0)

          = 4/-1

           = -4

Now use one of the point (-1, 2) in the graph and a general point (x,y) to find the function.

-4 = (y - 2)/(x - -1)

-4(x + 1) = y - 2

-4x - 4 = y - 2

y = -4x - 4 + 2

  = -4x - 2


∴ f(x) =  -4x - 2

6 0
3 years ago
A piece of wire 23 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral tria
AURORKA [14]

Answer:

For maximum area, all of the wire should be used to construct the square.

The minimum total area is obtained when length of the wire is 10m

Step-by-step explanation:

For maximum,  we use the whole length

For minimum,

supposed the x length was used for the square,

the length of the side of the square = x/4m

Area = \frac{x^{2} }{16}

For the equilateral triangle, the length of the side =  \frac{23 - x}{3}

Area = \frac{\sqrt{3} }{4}  a^{2}  = \frac{\sqrt{3} }{4} (\frac{23 - x}{3} )^{2}

Total Area = \frac{x^{2} }{16}  + \frac{\sqrt{3} }{36} (23-x)^{2}

\frac{dA}{dx}  = \frac{x}{8}  -  \frac{\sqrt{3} }{18} (23 - x)\\

\frac{d^{2}A }{dx^{2} }  = \frac{1}{8}  + \frac{\sqrt{3} }{18}  > 0, therefore it is minimum

\frac{dA}{dx}  = 0 \\\\

\frac{x}{8}  -  \frac{\sqrt{3} }{18} (23 - x) = 0\\

x = 10.00m

3 0
3 years ago
Read 2 more answers
Help I need the answers in 20 minutes
Gelneren [198K]

2. 5 hours

3. $200

4. 9.5 hours. If it has to be whole numbers, 10 hours

Hope that helps!

<em>-scsb17hm</em>

6 0
2 years ago
Read 2 more answers
Find the greatest common factor of -30 x4yz3 and 75 x4z2 .<br> ____x^? Z^?
Travka [436]

First find the common factor of -30 and 75, which is 15.

Next find the common factors of the variables:

The factors of x$6 is x*x*x*x

Factor for y is y

Factors for Z^3 is z*z*z

Factors for Z^2 is z*z

The GCF would be x^4z^2

Final answer = 15x^4z^2

7 0
2 years ago
Read 2 more answers
Jack and Jane are married and both work. However, due to their responsibilities at home, they have decided that they do not want
Sergeeva-Olga [200]
By setting up a system of equations we can easily solve this problem. Let's denote Jane's working hours with x and Jack's working hours with y. Since they don't want to work more than 65 hours, the first equation is x+y=65. The second equation is 14x+7y=770. By solving this system of equation \left \{ {{x+y=65} \atop {14x+7y=770}} \right., we find that y=20 hours, which is Jack's maximum working hours. 
6 0
3 years ago
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