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The functions
f(x)=-(x-4)^(2)+3 and
g(x)=-(x-4)^(2)+5 are graphed in the same
xy-plane as
y=f(x) and
y=g(x). If
(h_(1),k_(1)) is the vertex of the graph of function
f and
(h_(2),k_(2)) is the vertex of the graph of function
g, then what is
k_(2)-k_(1) ?
Choose 1 answer:
(A) -2
(B) 0
(c) 2
(D) 8

The functions $f(x)=-(x-4)^{2}+3$ and $g(x)=-(x-4)^{2}+5$ are graphed in the same $x y$ -plane as $y=f(x)$ and $y=g(x)$ . If $\left(h_{1}, k_{1}\right)$ is the vertex of the graph of function $f$ and $\left(h_{2}, k_{2}\right)$ is the vertex of the graph of function $g$ , then what is $k_{2}-k_{1}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $-2$ $\newline$ (B) $0$ $\newline$ (C) $2$ $\newline$ (D) $8$

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Compare linear and exponential growth

Full solution

Q. The functions

f(x)=-(x-4)^{2}+3

and

g(x)=-(x-4)^{2}+5

are graphed in the same

x y

-plane as

y=f(x)

and

y=g(x)

. If

\left(h_{1}, k_{1}\right)

is the vertex of the graph of function

f

and

\left(h_{2}, k_{2}\right)

is the vertex of the graph of function

g

, then what is

k_{2}-k_{1}

?

\newline

Choose

1

answer:

\newline

(A)

-2

\newline

(B)

0

\newline

(C)

2

\newline

(D)

8

Identifying the vertex of $f(x)$ : The question prompt is: ＂What is the difference in the $y$ -coordinates of the vertices of the graphs of the functions $f(x)$ and $g(x)$ ?＂
Identifying the vertex of g(x): First, let's identify the vertex of the graph of function f(x). The function f(x) is in the form of a parabola, $f(x) = a(x-h)^2 + k$ , where $(h, k)$ is the vertex of the parabola. For $f(x) = -(x-4)^2 + 3$ , the vertex $(h_1, k_1)$ is $(4, 3)$ .
Calculating the difference in y-coordinates: Next, let's identify the vertex of the graph of function $g(x)$ . The function $g(x)$ is also in the form of a parabola, $g(x) = a(x-h)^2 + k$ . For $g(x) = -(x-4)^2 + 5$ , the vertex $(h_2, k_2)$ is $(4, 5)$ .
Calculating the difference in y-coordinates: Next, let's identify the vertex of the graph of function $g(x)$ . The function $g(x)$ is also in the form of a parabola, $g(x) = a(x-h)^2 + k$ . For $g(x) = -(x-4)^2 + 5$ , the vertex $(h_2, k_2)$ is $(4, 5)$ .Now, we need to find the difference in the y-coordinates of the vertices of the two functions. This is calculated by subtracting $k_1$ from $k_2$ : $k_2 - k_1 = 5 - 3$ .
Calculating the difference in y-coordinates: Next, let's identify the vertex of the graph of function $g(x)$ . The function $g(x)$ is also in the form of a parabola, $g(x) = a(x-h)^2 + k$ . For $g(x) = -(x-4)^2 + 5$ , the vertex $(h_2, k_2)$ is $(4, 5)$ .Now, we need to find the difference in the y-coordinates of the vertices of the two functions. This is calculated by subtracting $k_1$ from $k_2$ : $k_2 - k_1 = 5 - 3$ .Performing the subtraction, we get $k_2 - k_1 = 5 - 3 = 2$ .

More problems from Compare linear and exponential growth

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Jill bought a used motorcycle from a seller online for $1,200. The seller will charge her $5 a day to store the motorcycle at his house until she is able to pick it up. You can use a function to describe the total amount of money Jill will owe the seller if she waits

x

days to pick up the motorcycle.

\newline

Write an equation for the function. If it is linear, write it in the form

g(x) = mx + b

. If it is exponential, write it in the form

g(x) = a(b)^x

\newline

g(x) = \underline{\hspace{3em}}

Posted 5 months ago

Question

f(t)=-2t-7

change over the interval from

t=-7

t=-6

\newline

\newline

\left[\text{f(t) decreases by } 2\right]

\newline

\left[\text{f(t) increases by } 2\right]

\newline

\left[\text{f(t) increases by } 200\%\right]

\newline

\left[\text{f(t) decreases by a factor of } 2\right]

Posted 5 months ago

Question

g(t)=9^t

change over the interval from

t=1

t=3

\newline

\newline

\left[\text{g(t) decreases by a factor of } 81\right]

\newline

\left[\text{g(t) increases by a factor of } 81\right]

\newline

\left[\text{g(t) increases by } 18\%\right]

\newline

\left[\text{g(t) decreases by } 9\%\right]

Posted 5 months ago

Question

Both of these functions grow as

x

gets larger and larger. Which function eventually exceeds the other?

\newline

\newline

(A)f(x) = 8x + 3.3

\newline

(B)g(x) = 3.3^x - 5

Posted 6 months ago

Question

Both of these functions grow as

x

gets larger and larger. Which function eventually exceeds the other?

\newline

\newline

(A) \ f(x) = 2x + 9

\newline

(B)\ g(x) = 2^x

Posted 6 months ago

Question

f(x)

g(x)

are differentiable.

\newline

h(x)

h(x)=\frac{g(x)}{f(x)}

\newline

f(8)=1

f'(8)=-6

g(8)=8

g'(8)=-10

h'(8)

\newline

Simplify any fractions.

\newline

h'(8)=

Posted 6 months ago

Question

p(x)

q(x)

are differentiable.

\newline

r(x)

r(x)= \frac{p(x)}{q(x)}

\newline

p(3)= 2

p'(3)= 4

q(3)= 6

q'(3)= 9

r'(3)

\newline

Simplify any fractions.

\newline

r'(3)=

Posted 7 months ago

Question

u(x)

v(x)

are differentiable.

\newline

w(x)

w(x)= \frac{u(x)}{v(x)}

\newline

u(5)= 3

u'(5)= -2

v(5)= 7

v'(5)= 1

w'(5)

\newline

Simplify any fractions.

\newline

w'(5)=

Posted 7 months ago

Question

a(x)

b(x)

are differentiable.

\newline

c(x)

c(x)= \frac{a(x)}{b(x)}

\newline

a(2)= 4

a'(2)= 5

b(2)= 1

b'(2)= -3

c'(2)

\newline

Simplify any fractions.

\newline

c'(2)=

Posted 7 months ago

Question

m(x)

n(x)

are differentiable.

\newline

o(x)

o(x)= \frac{m(x)}{n(x)}

\newline

m(7)= 2

m'(7)= -1

n(7)= 4

n'(7)= 8

o'(7)

\newline

Simplify any fractions.

\newline

o'(7)=

Posted 7 months ago

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