Find the vertex of the graph of the function. f(x) = (x - 5)2 + 10 (0, 5) (10, 0) (10, 5) (5, 10) question 2(multiple choice worth 1 points) find the vertex of the graph of the function. f(x) = 3x2 - 18x + 24 (4, -2) (-2, 4) (-3, 3) (3, -3) question 3(multiple choice worth 1 points) find the axis of the graph of the function. f(x) = 4x2 + 8x + 7 x = 3 x = -1 x = -2 x = 2 question 4(multiple choice worth 1 points) write the quadratic function in vertex form. y = x2 + 4x + 7 y = (x - 2)2 + 3 y = (x - 2)2 - 3 y = (x + 2)2 - 3 y =(x + 2)2 + 3 question 5(multiple choice worth 1 points) a projectile is thrown upward so that its distance above the ground after t seconds is h = -16t2 + 672t. after how many seconds does it reach its maximum height? 21 s 31.5 s 42 s 10 s question 6(multiple choice worth 1 points) find the zeros of the function. f(x) = 3x3 - 12x2 - 15x 1 and -5 0, -1, and 5 -1 and 5 0, 1, and -5

The correct options are  (1) (5,10), (2) (3,-3), (3) x = -1, (4) , (5) 21s and (6) 0, -1, and 5.

Explanation:

Te standard form of the parabola is,

       .....(1)

Where,  (h,k) is the vertex of the parabola.

(1)

The given equation is,

Comparing this equation with equation (1),we get,

and

Therefore, the vertex of the graph is (5,10) and the fourth option is correct.

(2)

The given equation is,

To make perfect square add , i.e., . Since there is factor 3 outside the parentheses, so subtract three times of 9.

Comparing this equation with equation (1),we get,

and

Therefore, the vertex of the graph is (3,-3) and the fourth option is correct.

(3)

The given equation is

To make perfect square add , i.e., . Since there is factor 4 outside the parentheses, so subtract three times of 1.

Comparing this equation with equation (1),we get,

and

The vertex of the equation is (-1,3) so the axis is x=-1 and the correct option is 2.

(4)

The given equation is,

To make perfect square add , i.e., .

Therefore, the correct option is  4.

(5)

The given equation is,

It can be written as,

It is a downward parabola. so the maximum height of the function is on its vertex.

The x coordinate of the vertex is,

Therefore,  after 21 seconds the projectile reach its maximum height and the correct option is first.

(6)

The given equation is,

Use factoring method to find the factors of the equation.

Equate each factor equal to 0.

Therefore, the zeros of the given equation is 0, -1, 5 and the correct option is 2.

the correct functions are

h(x) = 3x + 2  

g(x) = 2^x

step-by-step explanation:

i proceed to calculate the different values ​​of k (x)

case 1)  k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + > is the option  4. k(x) = 2^(3x + 2 )

case 2)  k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+> is the option  1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)

k(x) =  [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)

is the option  3.)   k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)

k(x) =  [2^x]-[3x + 2]=2^x-3x-> is the option  2.) k(x) = 2^x - 3x - 2 

case 5)  k(x) = g(x) × h(x)

k(x) = [2^x]*[3x + > is the option  5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)

h(x) ∘ g(x)=h(g(x))

k(x)=3*[2^x]+> is the option  6. k(x) = 3(2^x) +2