Distribute. 4(3x + 5)

Identify the vertex, axis of symmetry, minimum or maximum, domain, and range of the function f(

alekssr [168]

Identify the vertex, axis of symmetry, minimum or maximum, domain, and range of the function ()=−(+)^−

Answer:

vertex = (-4, -5)

Axis of symmetry = -4

use the (-4, -5) to find the minimum value

$Domain = ( - \infty, \infty ) , [ x | x\ is\ real ]\\\\Range = [ -5, \infty ), y\geq -5$

Solution:

Given function is:

$f(x) = (x+4)^2 - 5$

The equation in vertex form is given as:

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

Where, (h, k) is constant

On comparing give function with vertex form,

h = -4

k = -5

Vertex is (-4 , -5)

Axis of symmetry : x co-ordinate of vertex

Thus, axis of symmetry = -4

The coefficient of x^2 is positive in given function.

Thus the vertex point will be a minimum

$Minimum\ value = f(\frac{-b}{a})$

$f(x) = x^2 + 8x + 16 - 5\\\\f(x) = x^2 + 8x + 11$

$f(x) = ax^2+bx+c$

On comparing,

a = 1

b = 8

$x = \frac{-b}{2a} = \frac{-8}{2 \times 1} = -4$

$f(-4) = (-4)^2 + 8(-4) + 11 = 16 - 32 + 11 = -5$

Thus, use the (-4, -5) to find the minimum value

Domain and range

$f(x) = (x+4)^2 - 5$

The domain is the input values shown on the x-axis

The range is the set of possible output values f(x)

Therefore,

$Domain = ( - \infty, \infty ) , [ x | x\ is\ real ]\\\\Range = [ -5, \infty ), y\geq -5$

4 0

3 years ago

Find the dimensions of a rectangle with perimeter 112 m whose area is as large as possible. step 1 if a rectangle has dimensions

Veronika [31]

Please use the solution below:
Let P = perimeter, A = area
As provided above, a = xy and
We know that the formula to solve for the perimeter of a rectangle is P = 2x + 2y. Using the given 112m, we can solve the perimeter using the formula:
112 = 2x + 2y
56 = x + y

x = 56-y or y = 56-x
Let's solve the perimeter in terms of y using the formula below:
A = (56-y)(y)
Find the derivative of A = 56-y^2 to get the value of y.
dA/dy = 56-2y = 0
y = 56/2
y = 28
To find X, substitute the value of y in the equation x = 56 - y.
x = 56 - 28
Therefore, x = 28.
We can conclude that the figure is not a rectangle but a square.

7 0

3 years ago

a can contain 15/16 pound of vegetables . one serving of these vegetables weights 1/4 pound . whats is the total number of servi

Elodia [21]

1/4=4/16 so the can has 3 servings and a some leftovers that are smaller than a serving. I think the answer is 3.

5 0

3 years ago

does anyone know how to help me with the letters in math, i dont understand it, and i need help, someone please? if you can can

galina1969 [7]

Answer:

Step-by-step explanation:

Letters are variables and those variable can store a number

Ex: x=5 y=2

evaluate : 3x+2y

we know that x is 5, so we know that 3x would be 15

we know that y is 2, so we know that 2x would be 4

then it says to add 3x and 2y, we would add 15 and 4 to get 19

(This is a very simple example, when you get older, the expression would be much more confusing.

3 0

3 years ago

Read 2 more answers

Percents are the result of expressing numbers as a part of?

KonstantinChe [14]

If you mean you get them by diving them by 100 or something over 100(as in a fraction) that's the answer, I'm incredibly sorry if it is not what you meant!

4 0

3 years ago