1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Delvig [45]
2 years ago
14

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

Mathematics
1 answer:
stepan [7]2 years ago
8 0
\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.
You might be interested in
Terry evaluates 6 divided by 1/8 using multiplication expression
Volgvan

what is way two get to the south pole.

6 0
2 years ago
H(t)=-16(t-1)^2+16 <br> What is the maximum height the ball reaches and how long does it take?
Aleksandr-060686 [28]

Given t = time and h = height

h(t) =  - 16(t - 1)^{2}  + 16

From the equation.

y = a(x - h)^{2}  + k

h is the axis od symmetry

(h, k) is the vertex.

In the equation, h is 1 and k is 16.

So the maximum value is 16 at t = 1.

The ball reaches maximum at 16 and it takes t = 1 to reach the maximum point.

4 0
2 years ago
According to the video, this career offers a good opportunity to do what?
ZanzabumX [31]

Answer:

im not sure for this but i think its build friendships with customers

6 0
3 years ago
What is the answer plsssss help
Sergeu [11.5K]

Answer:

f=9 x 20

Step-by-step explanation:

7 0
3 years ago
A rectangular restaurant kitchen has a perimeter of 36 meters and an area of 80 square meters. what are the dimensions of the ki
konstantin123 [22]
Let L and W be the length and width of the given rectangle, respectively. Perimeter is calculated through the equation,

    P = 2L + 2W

Substituting the perimeter,
   36 = 2L + 2W
Simplifying,
    18 = L + W

The area is calculated by multiplying the length and width as below,
    A = 80 = LW
  
Substituting the expressions,
   80 = (L)(18 - L)
The value of L from the equation is 8. With this, the value of W is equal to 10.

Therefore, the dimensions of the rectangle are 8 m by 10 m. 
8 0
3 years ago
Other questions:
  • Anybody know ? 9&amp; 10
    15·1 answer
  • Name the property illustration<br><br> a + c + 2b = a + 2b + c
    8·1 answer
  • NEED ANSWERED ASAP!!
    10·2 answers
  • To add or subtract values written in scientific notation, the numbers must have the same______of 10
    15·1 answer
  • For the data set below, which of the following are true? {88, 79, 86, 93, 76, 80, 82, 72, 95, 79}
    15·1 answer
  • Find the equation of the line that passes through a point A(1,-5) B(-2,-7) ​
    11·1 answer
  • Solve by factoring <br> 15x^2 - 25x =0
    7·1 answer
  • The average of 5 integers is 8. Find the sum of the integers<br>it's pretty urgent
    12·1 answer
  • If you spin a quarter in space what type of 3D figure would you
    11·1 answer
  • Which three lengths can be the lengths of the sides of a triangle? Choose all that apply.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!