Mathematics, 02.07.2019 01:00, Homepage10

Identify the vertex, axis of symmetry, maximum or minimum and domain and range of each function 1. f(x)=4(x+2)^2-6 2. f(x)=10(x-1)^2+5

Answers: 1

Show answers

Answers

For first function vertex is (-2,-6), axis of symmetry is x = -2, minimum at (-2,-6), domain is all real numbers and range is $[-6,\infty)$ . For second function vertex is (-1,5), axis of symmetry is x = -1, minimum at (-1,5), domain is all real numbers and range is $[5,\infty)$ .

Explanation:

The standard for of the parabola is,

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

Where (h,k) is vertex and vertex is the extreme point of a parabola. The axis of symmetry is y=h. If a>0 then f(x) is minimum at (h,k) and if a<0 then f(x) is maximum at (h,k).

The first function is,

f(x)=4(x+2)^2-6

On comparing this equation with standard form of parabola we get,

h=-2,k=-6,a=4 0

Therefore, the vertex is (-2,-6), axis of symmetry is x = -2, minimum at (-2,-6).

The function defined for all values of x, so the domain of f(x) is all real numbers. Since the minimum value of the function is -6, therefore range must be greater than or equal to -6.

The second function is,

f(x)=10(x-1)^2+5

On comparing this equation with standard form of parabola we get,

h=-1,k=5,a=10 0

Therefore, the vertex is (-1,5), axis of symmetry is x = -1, minimum at (-1,5).

The function defined for all values of x, so the domain of f(x) is all real numbers. Since the minimum value of the function is 5, therefore range must be greater than or equal to 5.

answered: Guest

i = 2 / - 5

step-by-step explanation:

evaluation of ( 2 - 4 ) ( p + q ) when p = 2 and q = 5 i, by putting values of p and q,

0 = ( 2 - 4 ) ( p + q )0 = ( 2 - 4 ) ( 2 + 5 i ), by multiplying these0 = ( 4 + 10 i - 8 - 20 i )0 = 4 - 8 + 10 i - 20 i0 = - 4 -10 i 0 = 2 ( - 2 - 5 i )0 / 2 = - 2 - 5 i- 2 - 5 i = 0- 5 i = 2i = 2 / - 5

answered: Guest

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 16:30, emilyanneK2540

Jackie purchased 3 bottles of water and 2 cups of coffee for a family for $7.35. brian bought 4 bottles of water and 1 cup of coffee for his family for $7.15. how much does each bottle of water cost? how much does each cup of coffee cost? i need this done

Answers: 3

continue

Mathematics, 21.06.2019 17:30, lexusdixon3

Sheila wants to bake six muffins but the recipe is for 12 muffins . this means you only need half of the ingredients listed how much of the of each ingredient does she need? one cup and banana chips ,7 tablespoons oil , two eggs, 3/4 cups flour 1/4 cup walnuts show all you work and justify your answer using a baby toulmin.

Answers: 3

continue

Mathematics, 21.06.2019 18:00, tasnimsas3

Plz a. s. a. p. the table shows the number of male and female contestants who did not win a prize. what is the probability that a randomly selected contestant won a prize, given that the contestant was female? write the probability as a percent. round to the neares tenth, if needed.

Answers: 1

continue

Mathematics, 21.06.2019 19:00, mylittleponeyfbrarit

When keisha installed a fence along the 200 foot perimeter of her rectangular back yard, she left an opening for a gate. in the diagram below, she used x to represent the length in feet of the gate? what is the value? a. 10 b. 20 c. 25 d. 30

Answers: 1

continue

Do you know the correct answer?

Identify the vertex, axis of symmetry, maximum or minimum and domain and range of each function 1. f...