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
Anna35 [415]
3 years ago
13

Transforming quadratic graphs

Mathematics
1 answer:
rewona [7]3 years ago
8 0

Answer:

f(x) = 3(x - 2)² + 4

OR  

f(x) = 3x² - 12x + 16

Step-by-step explanation:

Vertex form of a parabola:

  • y = a(x - h)² + k

Standard form of a parabola:

  • y = ax² + bx + c

Let's find the vertex of this parabola.

  • (h, k) → (2, 4)

In order to find the a-value (vertex form), let's use another point besides the vertex on the parabola.

Using (3, 7) for (x, y), let's substitute this point and the vertex (2, 4) for (h, k) into the vertex form equation and solve for a.

  • 7 = a[(3) - (2)]² + 4

Simplify using PEMDAS.

  • 7 = a(1)² + 4
  • 7 = a + 4

Subtract 4 from both sides.

  • a = 3

Now we have (h, k) and a of the vertex form.

  • y = a(x - h)² + k  → y = 3(x - 2)² + 4

In order to convert from vertex to standard form, simplify the equation by FOILing.

  • y = 3(x - 2)² + 4
  • y = 3(x² - 4x + 4) + 4

Distribute 3 inside the parentheses.

  • y = 3x² - 12x + 12 + 4

Combine like terms.

  • y = 3x² - 12x + 16

Therefore, we have the answer:

<u>Vertex form:</u>

  • f(x) = 3(x - 2)² + 4

<u>Standard form:</u>

  • f(x) = 3x² - 12x + 16
You might be interested in
Six decreased by 9 times a number is -39
Andrew [12]

The translation of the mathematical statement given as six decreased by 9 times a number is -39 is 9x - 6 = -39

<h3>How to translate the mathematical statement?</h3>

The mathematical statement is given as:

six decreased by 9 times a number is -39

9 times a number means

9 * x (assume x is the number)

So, we have:

six decreased by 9 times a number is -39 ⇒ six decreased by 9x is -39

Decreased by means we subtract 6 from 9x.

So, we have:

six decreased by 9 times a number is -39 ⇒ 9x - 6 = -39

Hence, the translation of the mathematical statement given as six decreased by 9 times a number is -39 is 9x - 6 = -39

Read more about mathematical statement at

brainly.com/question/4541471

#SPJ1

5 0
1 year ago
I need help on this algebra oneeeee
True [87]
The answer of above equation is f
7 0
3 years ago
You need to buy some chicken for dinner tonight. You found an ad showing that the store across town has it on sale for $2.79 a p
san4es73 [151]

Answer:

B) Going to the close store is cheaper.

Step-by-step explanation:

Cost of going to the next town:

(8.3mi/22mi) × $3.79 = $1.43

Cost of going to the close store:

(2.3mi/22mi) × $3.79 = $0.40

3 0
3 years ago
{x|x€Z^x&lt;8}<br> Please someone help me what should be the elements in the set
joja [24]
What how is this a problem and how are you in middle school

5 0
3 years ago
Which is the area of a rectangle with a length of 21 feet and a width of 15 feet?
MA_775_DIABLO [31]

Answer:

315

Step-by-step explanation:

Area = Length x Width

Area = 21 x 15

Area = 315

3 0
3 years ago
Read 2 more answers
Other questions:
  • Solve: 2x + 27 = 3x - 9
    15·1 answer
  • 3x - 8 &lt; -2x +22 solve the inequality
    12·2 answers
  • What is the volume of the pyramid 5m 5m 3m 4 m
    7·1 answer
  • .Which of these numbers are factors of 9? Check all that apply. 1 2 3 9 18
    15·1 answer
  • How many quarts are equivalent to 14 liters? Round your answer to the nearest tenth.
    9·2 answers
  • Can someone help me with this excercises plz:
    11·1 answer
  • When asked to dilate a shape By a scale factor of 1/3 will the shape become larger or smaller?
    15·1 answer
  • Please due in 1 hour
    7·2 answers
  • Suppose that 29\%29%29, percent of undergraduates at a large university are involved in a campus organization. The administratio
    5·1 answer
  • What is the slope of a line that goes through the points (3, 7) and (8, 11)
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!