Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Write the new equation for
y=sin(x) given the following change:
(3 pts.)
a. Moved up
2quad y=
qquad
b. Reflected across
y-axis

y=

qquad
c. Stretched vertically by a factor of 3

y=

qquad

$8$ . Write the new equation for $y=\sin (x)$ given the following change: $\newline$ ( $3$ pts.) $\newline$ a. Moved up $2 \quad y=$ $\qquad$ $\newline$ b. Reflected across $y$ -axis $\newline$ $y=$ $\newline$ $\qquad$ $\newline$ c. Stretched vertically by a factor of $3$ $\newline$ $y=$ $\newline$ $\qquad$

View step-by-step help

View step-by-step help

Transformations of quadratic functions

Full solution

Q.

8

. Write the new equation for

y=\sin (x)

given the following change:

\newline

(

3

pts.)

\newline

a. Moved up

2 \quad y=

\qquad

\newline

b. Reflected across

y

-axis

\newline

y=

\newline

\qquad

\newline

c. Stretched vertically by a factor of

3

\newline

y=

\newline

\qquad

Move Up $2$ Units: a. Moved up $2$ units. $\newline$ To move the graph up, add $2$ to the original function. $\newline$ $y = \sin(x) + 2$
Reflect Y-Axis: b. Reflected across the y-axis. $\newline$ To reflect across the y-axis, replace $x$ with $-x$ in the original function. $\newline$ $y = \sin(-x)$ $\newline$ But since $\sin(-x) = -\sin(x)$ , the equation becomes: $\newline$ $y = -\sin(x)$
Stretch Vertically by $3$ : c. Stretched vertically by a factor of $3$ . $\newline$ To stretch the graph vertically, multiply the original function by $3$ . $\newline$ $y = 3\sin(x)$

More problems from Transformations of quadratic functions

Question

Solve by completing the square.

\newline

m^2 - 10m - 29 = 0

\newline

Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

\newline

`m` = ____ or `m` = _____

Posted 1 month ago

Question

g(x)

g(x)

is the translation

5

f(x)=x^2

\newline

Write your answer in the form

a(x–h)^2+k

a

h

k

\newline

g(x)=

Posted 1 month ago

Question

What is the range of this quadratic function?

\newline

y = x^2 - 4x + 4

\newline

\newline

\left\{y \mid y \geq 2\right\}

\newline

\left\{y \mid y \leq 0\right\}

\newline

\left\{y \mid y \geq 0\right\}

\newline

\text{all real numbers}

Posted 1 month ago

Question

Write the equation of the parabola that passes through the points

(1,0)

(2,0)

(3,\text{–}16)

. Write your answer in the form

y = a(x – p)(x – q)

a

p

q

are integers, decimals, or simplified fractions.

\newline

Posted 1 month ago

Question

Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.

\newline

f^2 + 8f + \_\_\_\_\_

Posted 1 month ago

Question

h

\newline

h^2 + 39h = 0

\newline

\newline

Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.

\newline

h =

\newline

Posted 1 month ago

Question

Write a quadratic function with zeros

-9

-7

\newline

Write your answer using the variable

x

and in standard form with a leading coefficient of

1

\newline

f(x) = \_\_\_\_\_

Posted 2 months ago

Question

Find the equation of the axis of symmetry for the parabola

y = x^2

\newline

Simplify any numbers and write them as proper fractions, improper fractions, or integers.

\newline

\underline{\hspace{3cm}}

Posted 2 months ago

Question

g(x)

g(x)

is the translation

8

f(x) = x^2

\newline

Write your answer in the form

a(x – h)^2 + k

a

h

k

\newline

g(x) =

\newline

Posted 2 months ago

Question

x

\newline

x^2 = 1

\newline

\newline

Write your answer in simplified, rationalized form.

\newline

x =

x =

\newline

Posted 2 months ago