Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

f(x)=x^(2)-6x-7
Which of the following is an equivalent form of the function
f in which the zeros of
f appear as constants or coefficients?
Choose 1 answer:
(A)
f(x)=(x-7)(x+1)
(B)
f(x)=(x-1)(x+7)
(c)
f(x)=x(x-6)-7
(D)
f(x)=(x-6)^(2)-7

$f(x)=x^{2}-6 x-7$ $\newline$ Which of the following is an equivalent form of the function $f$ in which the zeros of $f$ appear as constants or coefficients? $\newline$ Choose $1$ answer: $\newline$ (A) $f(x)=(x-7)(x+1)$ $\newline$ (B) $f(x)=(x-1)(x+7)$ $\newline$ (C) $f(x)=x(x-6)-7$ $\newline$ (D) $f(x)=(x-6)^{2}-7$

View step-by-step help

View step-by-step help

Compare linear and exponential growth

Full solution

Q.

f(x)=x^{2}-6 x-7

\newline

Which of the following is an equivalent form of the function

f

in which the zeros of

f

appear as constants or coefficients?

\newline

Choose

1

answer:

\newline

(A)

f(x)=(x-7)(x+1)

\newline

(B)

f(x)=(x-1)(x+7)

\newline

(C)

f(x)=x(x-6)-7

\newline

(D)

f(x)=(x-6)^{2}-7

Find Zeros: To find an equivalent form of the function that shows the zeros, we need to factor the quadratic equation $f(x) = x^2 - 6x - 7$ . $\newline$ We look for two numbers that multiply to $-7$ and add up to $-6$ . $\newline$ The numbers $-7$ and $+1$ satisfy these conditions because $(-7) \times (+1) = -7$ and $(-7) + (+1) = -6$ .
Factor Quadratic Equation: We use these numbers to factor the quadratic equation: $\newline$ f(x) = $x^2 - 6x - 7$ $\newline$ f(x) = $(x - 7)(x + 1)$ $\newline$ This is the factored form of the quadratic equation, which reveals the zeros of the function.
Compare with Answer Choices: We compare the factored form with the given answer choices to find the matching one. $\newline$ (A) $f(x) = (x - 7)(x + 1)$ matches the factored form we found in Step $2$ .
Compare with Answer Choices: We compare the factored form with the given answer choices to find the matching one. $\newline$ (A) $f(x) = (x - 7)(x + 1)$ matches the factored form we found in Step $2$ .We check the other answer choices to confirm that they do not match the factored form we found: $\newline$ (B) $f(x) = (x - 1)(x + 7)$ does not match because it would expand to $x^2 + 6x - 7$ . $\newline$ (C) $f(x) = x(x - 6) - 7$ does not match because it would expand to $x^2 - 6x - 7$ , but does not show the zeros as constants or coefficients. $\newline$ (D) $f(x) = (x - 6)^2 - 7$ does not match because it would expand to $x^2 - 12x + 36 - 7$ .

More problems from Compare linear and exponential growth

Question

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 8 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 8 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 8 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 9 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 9 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 8 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 9 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 9 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 9 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 9 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant