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
34kurt
3 years ago
6

Write an equation that has a graph with the shape of y = x^2, but shifted left 3 units.

Mathematics
1 answer:
svetoff [14.1K]3 years ago
6 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 % template detailing
\bullet \textit{ stretches or shrinks horizontally by  } {{  A}}\cdot {{  B}}\\\\
\bullet \textit{ flips it upside-down if }{{  A}}\textit{ is negative}
\\\\
\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}\\\\

\bf \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}}}

now, with that template in mind, let's see

\bf y=x^2\implies 
\begin{array}{llll}
y=(&1x&-0)^2\\
&B&C
\end{array}

so, just change C to +3, thus C/B is 3/1
You might be interested in
Solve the following problems : Given: S, T, and U are the midpoints of RP , PQ , and QR respectively. Prove: △SPT≅△UTQ.
AleksandrR [38]

Answer:

Hence Proved △ SPT ≅ △ UTQ

Step-by-step explanation:

Given: S, T, and U are the midpoints of Segment RP , segment PQ , and segment QR respectively of Δ PQR.

To prove: △ SPT ≅ △ UTQ

Proof:

∵ T is is the midpoint of PQ.

Hence PT = PQ    ⇒equation 1

Now,Midpoint theorem is given below;

The Midpoint Theorem states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.

By, Midpoint theorem;

TS║QR

Also, TS = \frac{1}{2} QR

Hence, TS = QU (U is the midpoint QR) ⇒ equation 2

Also by Midpoint theorem;

TU║PR

Also, TU = \frac{1}{2} PR

Hence, TU = PS (S is the midpoint QR) ⇒ equation 3

Now in △SPT and △UTQ.

PT = PQ (from equation 1)

TS = QU (from equation 2)

PS = TU (from equation 3)

By S.S.S Congruence Property,

△ SPT ≅ △ UTQ ...... Hence Proved

6 0
3 years ago
Which type of graph would be most appropriate to help you organize a set of data in numerical order?
mixer [17]
A bar graph or line graph. Hope I helped!!
5 0
3 years ago
Read 2 more answers
What container would logically hold 1000 liters<br> i need to know in next five minute!!!
valkas [14]
A storage tank. I hope this helps ^^
3 0
3 years ago
(1×1)-tan×(-tan) evaluate it by Determinants
andrew11 [14]

Answer:

1x1

Step-by-step explanation:

4 0
3 years ago
In a right triangle one leg measures a quarter of the other, how much do its acute angles measure? with procedure please​
KATRIN_1 [288]

Answer:

The answer to your question is 14° and 76°

Step-by-step explanation:

Data

leg 1 = x

leg 2 = x/4

angle 1 = ?

angle 2 = ?

Process

To solve problem use trigonometric functions. We must use the trigonometric function that relates both legs (tangent).

    tangent Ф = Opposite side / Adjacent side

-Substitution

    tan Ф = (x/4) / x

-Simplification

    tan Ф = x / 4x

    tan Ф = 1/4

-  Find Ф

     Ф = tan⁻¹(1/4) =  14°

- Find the other acute angle

  The sum of the internal angles in a triangles equals 180°

       Ф + Ф₁ + 90° = 180

-Solve for Ф₁

        Ф₁  = 180 - 90 - 14

-Result

        Ф₁ = 76°              

3 0
3 years ago
Other questions:
  • A cola company wants to test their cola against their biggest competitor's cola. They decide to randomly sample 150 people. The
    5·1 answer
  • What are the like terms and coefficients in 2m+3m-m
    15·1 answer
  • What is the equation of a line that is parallel to the line whose equation is y = x + 2?a.x + y = 5b.2x + y = −2c.y − x = −1d.y
    13·1 answer
  • Selma uses a jogging trail that runs through a park near her home. The trail is a loop that is of a mile long. On Monday, Selma
    7·2 answers
  • Find a cartesian equation for the curve and identify it. r = 10 tan(θ) sec(θ)
    7·1 answer
  • What line is parallel to y=1/2x+5
    15·1 answer
  • Janie and Jasmine are playing three games at an arcade. Each of the games requires either 2, 3, or 4 tokens. The girls plan to p
    14·1 answer
  • An Internet company reported that its earnings will be less than the 24 cents per share that was predicted. Write an inequality
    6·2 answers
  • SOMEONE PLZ HELP I HAVE TILL TMR TO GET A 49% up
    12·1 answer
  • X is greater than or equal to -7. Can-7 be a solution for x? Explain
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!