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
Sonbull [250]
3 years ago
11

After transforming f(x) = 2x² +4x + 3 into vertex form, the vertex is easily identifiable. Which ordered pair is the vertex?

Mathematics
1 answer:
jolli1 [7]3 years ago
7 0

The vertex is (-1,1)

Explanation:

The equation is f(x)=2x^{2} +4x+3

To find the vertex, we need the equation in the form of f(x)=a (x-h)^{2}+k

Dividing each term by 2 in the equation f(x)=2x^{2} +4x+3

f(x)=2(x^{2} +2x+\frac{3}{2} )

Now, completing the square by adding and subtracting 1, we get,

f(x)=2(x^{2} +2x+1-1+\frac{3}{2} )

The first three terms can be written as (x+1)^{2},

f(x)=2[(x+1)^{2}+\frac{1}{2}  ]

Multiplying 2 into the bracket, we get,

f(x)=2(x+1)^{2} +1

This equation is of the form f(x)=a (x-h)^{2}+k

Now, we shall find the vertex (h,k)

Thus, h=-1 and k=1

Thus, the vertex is (-1,1)

You might be interested in
ΔCAR has coordinates C (2, 4), A (1, 1), and R (3, 0). A translation maps point C to C' (3, 2). Find the coordinates of A' and R
shutvik [7]

Answer:

A'= (2,-1) and R'=(4,-2) under this translation.

Step-by-step explanation:

A translation in R^{2} is a mapping T from R^{2} to R^{2}  defined by T(x,y) = (x + v_1,y+v_2), where v=(v_1,v_2) is a fixed vector in R^{2}.

From the problem we know that T(2,4)=(3,2), so we need to find the values v_1 and v_2 such that  T(2,4) = (2 + v_1,4+v_2)=(3,2), so 3=2 + v_1 and 4+v_2=2, thus v_1=1 and v_2=2.

Then T(x,y) = (x + 1,y-2) and  

T(1,1)=(1+1,1-2)=(2,-1)=A'

T(3,0)=(3+1,0-2)=(4,-2)=R'

Therefore A'= (2,-1) and R'=(4,-2). The triangles CAR and C'Q'R' are shown in the figure below.

7 0
3 years ago
one positive integer is 2 less than another. The product of the two integers is 24. what are the two integers?
irinina [24]

If one is positive we can conclude that the other is also positive

Positive*positive=positive(24)

The product of the two numbers is 24

And the smaller number is less than the greater number by 2

Factors of 24=1*24,2*12,3*8,4*6.

The only pair with the diffrence of two is 4*6

Therefore the two integers are 4 and 6

4 0
2 years ago
Go Math plz try your best
rosijanka [135]
108÷6 = 18 and 84÷6=14 last one is 184÷8=23
4 0
3 years ago
Geometry Grade 10
Tom [10]

Answer:

8, 4, and 2 can not be the lengths of the sides of a triangle.

Step-by-step explanation:

If a and b are the two side's length of a triangle then the length of the third line (c) will be governed by the relation  

(a+ b) > c > (a - b)

Now, the two sides length of a triangle are given by 8 and 4 then the length of the third side (x) will be given by  

(8 + 4) > x > (8 - 4)

⇒ 12 > x > 4 ........... (1)

But here the third side length is 2 which does not satisfy the above condition (1).

Hence, a triangle can not have side lengths 8, 4, and 2. (Answer)

4 0
3 years ago
I don’t get this at all :(
Readme [11.4K]

You do not get what

Hope this is helpful

8 0
3 years ago
Other questions:
  • The longer base of an isosceles trapezoid measures 23 ft. The nonparallel sides measure 9 ft, and the base angles measure 80°. F
    12·2 answers
  • Solve for x<br><br><br> 6x−2(x+4)=12
    9·2 answers
  • Sandy is helping her uncle at this coffee shop. She observes that, when ordering coffee, 13 of customers select chocolate flavor
    9·1 answer
  • Which of the following equations represent linear functions?
    15·1 answer
  • Construct the perpendicular bisector of the following segments.
    14·1 answer
  • What is the value of this expression when b=5?<br><br> 6(2b-4)
    10·2 answers
  • Carina's car averages 25 miles per gallon.Will she be able to make the round trip on one tank of gas.
    9·1 answer
  • DO ANYONE KNOW HOW TI FIND THE AREA OF A REGULAR POLYGON?? ill give brainlest and points​
    15·2 answers
  • Assume that adults have IQ scores that are normally distributed with a mean of μ= 105 and a standard deviation Ï =20 . Find the
    14·1 answer
  • Domain of y=5x+2 help!!!!
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!