6x6x6x6x6........................

The graph of f(x) = x^2 has been shifted into the form f(x) = (x − h)^2 + k

stepan [7]

$\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\\\
% left side templates
\begin{array}{llll}
f(x)=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
y=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
f(x)=&{{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}}(\mathbb{R})^{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}} sin\left({{ B }}x+{{ C}} \right)+{{ D}}
\end{array}\\\\
--------------------\\\\$

$\bf \bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\
\bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\
\left. \qquad \right. \textit{reflection over the x-axis}
\\\\
\bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\
\left. \qquad \right. \textit{reflection over the y-axis}$

$\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\
\left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\
\left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\
\bullet \textit{ vertical shift by }{{ D}}\\
\left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\
\left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{{{ B}}}$

with that template in mind, let's see, it went to the right 2 units, and then up 3 units.

that simply means, C = -2, D = 3.

8 0

2 years ago

Triangle PQR lies in the xy-plane, and the coordinates of vertex Q are (2, –3). Triangle PQR is rotated 180° clockwise about the

trasher [3.6K]

Answer:

(2,3)

Step-by-step explanation:

We are given that triangle PQR lies in the xy-plane, and coordinates of Q are (2,-3).

Triangle PQR is rotated 180 degrees clockwise about the origin and then reflected across the y-axis to produce triangle P'Q'R',

We have to find the coordinates of Q'.

The coordinates of Q(2,-3).

180 degree clockwise rotation about the origin then transformation rule

$(x,y)\rightarrow (-x,-y)$

The coordinates (2,-3) change into (-2,3) after 180 degree clockwise rotation about origin.

Reflect across y- axis the transformation rule

$(x,y)\rightarrow (-x,y)$

Therefore, when reflect across y- axis then the coordinates (-2,3) change into (2,3).

Hence, the coordinates of Q(2,3).

5 0

2 years ago

walmart sells the bike he likes for 350 dollars Walmart had the bike on sell for 30% off what is the cost of the bike at Walmart

lara31 [8.8K]

Answer:

$245

Step-by-step explanation:

350× 0.30 = 105 dollars off

350-105 = 245

7 0

2 years ago

Read 2 more answers

Calculate the ending balance of your savings account if you deposit $400 and earn simple interest a 7% for five years.

masha68 [24]

Okay well 7%, changes into 7/100=0.07 and there are 5 years and you have the beginning amount of 400. So 400×0.07=28. 28×5= 140. So add 140 to the be amount, 400+140=$540. Answer is $540.

6 0

2 years ago

Four friends are creating posters for their presentations, which will be delivered in different locations. Which person should c

Evgen [1.6K]

Answer:

Lindsey, who is delivering her speech in a large auditorium

Step-by-step explanation:

Jin, who is delivering her speech to a small group sitting around a table

Lindsey, who is delivering her speech in a large auditorium

Luke, who is delivering his speech in a typical classroom

Jordan, who is delivering his speech in a small meeting room

8 0

2 years ago