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
Ivanshal [37]
3 years ago
11

write the equation of the parabola and a vertex form and standard form given the following information​

Mathematics
2 answers:
Andreas93 [3]3 years ago
6 0

Answer:  9) y = 5(x - 3)² - 2         y = 5x² - 30x + 43

              10) y = (x - 2)² - 5           y =  x² - 4x + 2

<u>Step-by-step explanation:</u>

The Vertex form of a quadratic equation is:    y = a(x - h)² + k     where

  • "a" is the vertical stretch
  • (h, k) is the vertex
  • (x, y) is any point on the parabola

The Standard form of a quadratic equation is: y = ax² + bx + c

--> this is found by expanding the vertex form and adding like terms.

Input Vertex (h, k) and Point (x, y) into the Vertex form to solve for "a"

9) Vertex (h, k) = (3, -2) and Point (x, y) = (2, 3)

   3 = a(2 - 3)² - 2

  3 = a(-1)² - 2

  5 = a(1)

  5 = a

Vertex form: y = 5(x - 3)² - 2

Standard Form: y = 5(x² - 6x + 9) - 2

                          y = 5x² - 30x + 45 - 2

                          y = 5x² - 30x + 43

10) Vertex (h, k) = (2, -5) and Point (x, y) = (5, 4)

  4 = a(5 - 2)² - 5

  4 = a(3)² - 5

  9 = a(9)

  1 = a

Vertex form: y = (x - 2)² - 5

Standard Form: y = (x² - 4x + 4) - 2

                          y =  x² - 4x + 2

                         

beks73 [17]3 years ago
4 0

Answer:

see explanation

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

(9)

Here (h, k) = (3, - 2), thus

y = a(x - 3)² - 2

To find a substitute (2, 3) into the equation

3 = a(2 - 3)² - 2 ( add 2 to both sides )

5 = a(- 1)² = a , then

y = 5(x - 3)² - 2 ← in vertex form

y = 5(x² - 6x + 9) - 2

   = 5x² - 30x + 45 - 2

y = 5x² - 30x + 43 ← in standard form

(10)

Here (h, k) = (2, - 5), thus

y = a(x - 2)² - 5

To find a substitute (5, 4) into the equation

4 = a(5 - 2)² - 5 ( add 5 to both sides )

9 = a(- 3)² = 9a ( divide both sides by 9 )

a = 1

y = (x - 2)² - 5 ← in vertex form

y = x² - 4x + 4 - 5

y = x² - 4x - 1 ← in standard form

You might be interested in
Hey everybody just checking in if you say hi I’ll give BRAINLIEST!
nordsb [41]
Hi... how are you ?
3 0
3 years ago
Read 2 more answers
A spinner has three colors: red, blue, abd yellow. The red and blue sectors are the same size. If you spin twice, the probabilit
givi [52]

Answer:

36%

Step-by-step explanation:

Red and blue is 8%

and= multiply

0.08 unmultiply = 0.64 or 64%

yellow = 100-64= 36%

5 0
3 years ago
Which of the following number sentences is true?<br> A -9=9<br> B-9=-(9)<br> C 9=(-9)<br> D 9=-(-9)
kondaur [170]

Answer:

A and D are the true number sentences

3 0
3 years ago
What is -19 + 37?<br> -56<br> -18<br> 18<br> 56
rodikova [14]
All your doing here is 37-19 adding negative is the same has munising 

So 37-19=18
5 0
3 years ago
Which of the following rational functions is graphed below?
lukranit [14]

<h2>1 \: root \: solving\: f(x) = 0 \\ x = 0 \\  \\ vertical \: asymptote \: at \\ x = 1 \:  \:  \: and \:  \:  \: x =  - 4 \\  \\ f(x) =  \frac{x}{(x  + 4)(x - 1)}</h2><h2>Option C</h2>

i just got a notification

4 0
1 year ago
Other questions:
  • A scale drawing of Jack's living room is shown below:
    9·2 answers
  • Points (2,7) ana (5,10).
    10·1 answer
  • Bethany purchases a stereo for $750. She pays $100 down and pays for the rest using financing. She is charged a $5
    10·1 answer
  • Solve each equation 6=1-2n+5
    9·1 answer
  • What is an equation of the line that passes through the point (2;8) and has a slope of 3?A.y= 3x-2
    12·2 answers
  • I don’t understand Help please???!!
    15·1 answer
  • What is the equation of the line in slope-intercept form
    11·1 answer
  • Estimate the unit rate to the nearest hundredth $,2.35 12 grade AA eggs​
    14·1 answer
  • Simplify:<br> (13x+4x) - (9x+3x)
    15·1 answer
  • Joe was driving on the highway a car ahead of him was driving far below the speed limit so he decided to pass. In the first seco
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!