All categories

2 years ago

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

You might be interested in

A function f(x)f(x) is graphed on the coordinate plane.

Effectus [21]

Answer

-4x - 2

Explanation

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!

-scsb17hm

6 0

2 years ago

Read 2 more answers

Find the greatest common factor of -30 x4yz3 and 75 x4z2 . ____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