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
Line p passes through A(-2, -4) and has a slope of 1/2 What is the standard form of the equation for line p?
yarga [219]
Point slope form is y-(-4) = 1/2(x-(-2)

y+4 =1/2 (x+2)

now the standard form 2y+8=x+2
so -x+2y=-6 is the equation for line p in standard form
4 0
3 years ago
What is the simplified expression for 2 (x minus 5)? 2 x Negative 10 x 2 x minus 10 2 x + 5
Kay [80]

Answer:

2x-10

Step-by-step explanation:

Multiply BOTH x and -5 by 2

7 0
3 years ago
Read 2 more answers
Please help solve the question in the image
____ [38]

Answer:

✅On average Albany gets 20.967 inches rain pee year and Zachary gets 25.153 inches rain per year.

✅On average, it rains more in Zachary in a year.

Step-by-step explanation:

Mean annual rainfall on average = total amount of rainfall for the period of years ÷ 10

✔️Mean Annual rainfall for Albany (in.):

= (22.82 + 19.83 + 28.40 + 23.35 + 30.78 + 21.34 + 11.20 + 17.04 + 18.63 + 16.28) ÷ 10

= 20.967

✔️Mean Annual rainfall for Zachary (in.):

= (26.41 + 23.54 + 30.02 + 26.35 + 34.24 + 25.74 + 18.98 + 21.26 + 23.61 + 21.38) ÷ 10

= 25.153

✅Therefore, on average Albany gets 20.967 inches rain pee year and Zachary gets 25.153 inches rain per year.

✅On average, it rains more in Zachary in a year.

7 0
3 years ago
Greatest to least <br> 5,-12/16,9/36,-23/35
Ksenya-84 [330]

Answer:

5, 9/36, -12/16, -23/35

Explanation:

Convert to decimals then rearrange.

6 0
2 years ago
Adult tickets to a basketball game cost $5. Student tickets cost $1. A total of $3,228 was collected on the
baherus [9]

Answer:

even im confused sory

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • What's the answer to (-1.4)+5.28
    11·2 answers
  • What is the simplest form of this expression? -5(-b+2)+7
    15·1 answer
  • Solve the inequality and graph the solution 2|x+1/3|&lt;9
    15·1 answer
  • On a coordinate plane, a dashed straight line with negative slope goes through (0, 1) and (2, negative 2). Everything to the lef
    12·2 answers
  • Best deal?2oz for 4.99 or 6oz for 9.85
    15·1 answer
  • A manufacturing company uses an acceptance scheme on items from a production line before they are shipped. The plan is a​ two-st
    13·1 answer
  • What is the term that is used for the only number which is neither positive nor negative.
    6·1 answer
  • the gross income is $215 per week the deductions are $15.16,$29.33,2%,1%,and 3% what is the net income
    13·1 answer
  • A parking lot that has 520 spaces
    13·2 answers
  • write an equation of the line slope intercept form that is parallel to Y= 1/2 X +3 and through the point (2, -1)
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!