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
Alexus [3.1K]
4 years ago
14

Complete the square in the quadratic function f given by f(x) = 2x2 - 6x + 4

Mathematics
1 answer:
4vir4ik [10]4 years ago
8 0

Completing the square is a way of factoring, and it is also a way to put a quadratic into vertex form to determine the vertex of the parabola. To begin completing the square, set the equation equal to 0 and then move the constant over by subtraction to get 2x^2-6x=-4. The rule for completing the square is that the leading coefficient has to be a 1. Ours is a 2. So we have to factor it out. 2(x^2-3x)=-4. We will take half the linear term, square it, and add it to both sides. Our linear term is 3. Half of 3 is 3/2 and 3/2 squared is 9/4. We add 9/4 inside the parenthesis. But outside is the 2 we factored out, hanging out front there, refusing to be ignored. It is a multiplier. That means what we have actually added in is 2*9/4 which is 18/4. That looks like this: 2(x^2-3x+\frac{9}{4})=-4+\frac{18}{4}. On the right we will do the addition there by finding a common denominator, but on the left we have, in this process, created a perfect square binomial, the whole point of this nightmare. That looks like this: 2(x-\frac{3}{2})^2=\frac{1}{2}. The only left to do, if you need to, is move the 1/2 back over to the other side of the equals sign and set the quadratic back equal to y. 2(x-\frac{3}{2})^2-\frac{1}{2}=y. The vertex of our parabola is (3/2, -1/2).

You might be interested in
Please help I only have 10 minutes left to submit this (:
olya-2409 [2.1K]

Answer:

A_{sector} = \dfrac{100\pi}{3}

A_{sector} = 104.7 ~square~units

Step-by-step explanation:

The area of a full circle is

A = \pi r^2

A full circle has a central angle of 360 degrees.

The area of a sector is a fraction of the area of a full circle and is proportional to the central angle of the sector.

For a sector:

A_{sector} = \dfrac{n}{360^\circ}\pi r^2

where n = central angle of sector.

Here you have a radius of 10 and a central angle of 120 deg.

A_{sector} = \dfrac{120^\circ}{360^\circ}\pi(10^2)

A_{sector} = \dfrac{1}{3}\pi(10^2)

A_{sector} = \dfrac{100\pi}{3} ~square~units

A_{sector} = 104.7 ~square~units

5 0
3 years ago
Jack has a fair coin. He tosses the coin four times. What is the probability that Jack gets heads, then heads, then tails, and t
Tcecarenko [31]
As you have a 1/2 chance of getting what you want when you flip the coin, to get heads, heads, tails, tails will be 1/2 x 1/2 x 1/2 x 1/2. Working our way down the line, 1/2 x 1/2 = 1/4, 1/4 x 1/2 = 1/8, and 1/8 x 1/2 = 1/16. Jack will get heads, heads, tails, tails 1/16 of the time.
7 0
3 years ago
Read 2 more answers
Why is there a general or standard form in maths?
kati45 [8]
Because there are different types of math used for different types of problems
7 0
3 years ago
Solve for x:<br> -3x +5 = 17
valentina_108 [34]

Answer:

x=-4

Step-by-step explanation:

-3x +5 = 17

-3x+5-5=17-5

    -3x=12

 -3x/3 = 12/-3

       x=-4

8 0
3 years ago
Solve for x ax+ b= r​
Alexxx [7]

Answer:

x = \dfrac{r - b}{a}

Step-by-step explanation:

ax + b = r

Subtract b from both sides.

ax = r - b

Divide both sides by a.

x = \dfrac{r - b}{a}

7 0
3 years ago
Other questions:
  • Can someone please help me on e and f i dont understand it and pls explain
    6·1 answer
  • Nine families went on a picnic. Each family had carried a cake for the picnic. 2/3 of each cake was eaten. Find out how much cak
    15·1 answer
  • A student is painting a room at a constant rate. She is able to paint 2/5 of a room in 1/2 of an hour. How long does it take to
    10·1 answer
  • Find the lengths of the sides of the rectangle if it is known that one of them is 14cm bigger than the other, and the diagonal o
    15·1 answer
  • A grocery store sells twelve water bottles for $13.80. A convenience store sells 10 water bottles for $11.80. Which store has th
    10·2 answers
  • How do you find theoretical probability?
    12·1 answer
  • What’s the answer? Pls help soon
    6·2 answers
  • Solve for x<br><br> |2x+1| + |3x-4| = 5
    5·1 answer
  • Dilate the figure by scale factor. Then enter the new coordinates.<br> K = 2
    8·2 answers
  • Using the following image, solve for SR. Look at the image closely.
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!