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
Genrish500 [490]
3 years ago
15

What would y=x^2 +x+ 2 be in vertex form

Mathematics
1 answer:
balu736 [363]3 years ago
7 0

Answer:

y = (x +  \frac{1}{2} )^{2}  +  \frac{7}{4}

Step-by-step explanation:

y =  {x}^{2}  + x + 2

We can covert the standard form into the vertex form by either using the formula, completing the square or with calculus.

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

The following equation above is the vertex form of Quadratic Function.

<u>Vertex</u><u> </u><u>—</u><u> </u><u>Formula</u>

h =  -  \frac{b}{2a}  \\ k =  \frac{4ac -  {b}^{2} }{4a}

We substitute the value of these terms from the standard form.

y = a {x}^{2}  + bx + c

h =  -  \frac{1}{2(1)}  \\ h =  -  \frac{ 1}{2}

Our h is - 1/2

k =  \frac{4(1)(2) - ( {1})^{2} }{4(1)}  \\ k =  \frac{8 - 1}{4}  \\ k =  \frac{7}{4}

Our k is 7/4.

<u>Vertex</u><u> </u><u>—</u><u> </u><u>Calculus</u>

We can use differential or derivative to find the vertex as well.

f(x) = a {x}^{n}

Therefore our derivative of f(x) —

f'(x) = n \times a {x}^{n - 1}

From the standard form of the given equation.

y =  {x}^{2}  +  x + 2

Differentiate the following equation. We can use the dy/dx symbol instead of f'(x) or y'

f'(x) = (2 \times 1 {x}^{2 - 1} ) + (1 \times  {x}^{1 - 1} ) + 0

Any constants that are differentiated will automatically become 0.

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

Then we substitute f'(x) = 0

0 =2x + 1 \\ 2x + 1 = 0 \\ 2x =  - 1 \\x =  -  \frac{1}{2}

Because x = h. Therefore, h = - 1/2

Then substitute x = -1/2 in the function (not differentiated function)

y =  {x}^{2}  + x + 2

y = ( -  \frac{1}{2} )^{2}  + ( -  \frac{1}{2} ) + 2 \\ y =  \frac{1}{4}  -  \frac{1}{2}  + 2 \\ y =  \frac{1}{4}  -  \frac{2}{4}  +  \frac{8}{4}  \\ y =  \frac{7}{4}

Because y = k. Our k is 7/4.

From the vertex form, our vertex is at (h,k)

Therefore, substitute h = -1/2 and k = 7/4 in the equation.

y = a {(x - h)}^{2}  + k \\ y = (x - ( -  \frac{1}{2} ))^{2}  +  \frac{7}{4}  \\ y = (x +  \frac{1}{2} )^{2}  +  \frac{7}{4}

You might be interested in
Jaquavion's grandfather cut 68 1/2 bales of hay from 2 fields. He cut 23 1/4 from 1 field. How many bales did he cut from the ot
Olin [163]
His grandfather cuts 45 1/4 bales of hay in the other field
4 0
3 years ago
Show the factors of 5 x y square + 7 x square y by tree diagram​
zlopas [31]

Answer:

Answer:

Domain = {x /x ≥ -7}

Step-by-step explanation:

The given function y =

Inside the square, negative will not come.

First let's find the domain. x + 7 must be greater than or equal to 0.

x + 7 ≥ 0

Solving x, we get

x ≥ -7

Domain = {x /x ≥ -7}

Hope this will help you.

3 0
3 years ago
The midpoint of AB is M(3,3). If the coordinates of A are (2,-8), what are the coordinates of B?
Lyrx [107]

Step-by-step explanation:

MID POINT =[(X1 +X2)/2 , (Y1 +Y2)/2]

WE KNKW THAT A(2,–8) AND THE MID POINT IS (3,3)

SUBSTITUTING INTO THE EQUATION ABOVE

(3,3) = [(2+ X2)/2 ,(–8+ Y2)/2]

EQUATING THE X COORDINATES

=> 3 = (2+ X2)/2 (CROSS MULTIPLY)

=> 6 = 2 + X2

X(subscript 2)= 4

EQUATING THE Y COORDINATES

=> 3 =(–8 +Y2)/2 (CROSS MULTIPLY)

6 = –8 +Y2

=> Y(subscript 2)= 14

THEREFORE THE COORDINATES OF B ARE (4 ,14)

hope this helps :)

4 0
3 years ago
What is 2,201,760 in word form
ludmilkaskok [199]
Two million,two hundred one thousand ,seven hundred sixty 
6 0
3 years ago
Kim planted sunflower seeds in a flower patch. The tallest sunflower grew 2.65 meters tall. The height of the shortest sunflower
eduard

Answer:

Its 2.31 meters

7 0
3 years ago
Other questions:
  • Consider the equation
    9·1 answer
  • The measure of one side of a square is (s + 3) inches. Write two different expressions to express the perimeter of this square.
    15·1 answer
  • Is (-5.-8) a solution of y &gt; 32 + 6 ?
    5·1 answer
  • An account had an initial deposit made and then interest was applied once a year at a fixed rate. The amount of money, in dollar
    12·1 answer
  • Estimate the x-values of critical points of f(x) on the interval 0
    13·1 answer
  • Jan's age is 3 years less than twice trits age. The sum of their ages is 30. Find their ages.
    6·1 answer
  • Explain why 51 is not a prime number​
    9·2 answers
  • Find the surface area of the shape below. Answer in NUMBERS only, NO units. Round your answer to the nearest tenth.
    9·1 answer
  • Aisha runs a tutoring business. With Plan 1, students may choose to pay $26 per hour. With Plan 2, they may follow the plan show
    13·1 answer
  • Is 7/12 greater than less than equal to 55%
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!