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
Leviafan [203]
3 years ago
13

Match the parabolas represented by the equations with their vertices. y = x2 + 6x + 8 y = 2x2 + 16x + 28 y = -x2 + 5x + 14 y = -

x2 + 7x + 7 y = 2x2 + 7x + 5 y = -2x2 + 8x + 5 Vertex Equation of Parabola (-1.75, -1.125) arrowRight (-3, -1) arrowRight (-4, -4) arrowRight (2.5, 20.25) arrowRight
Mathematics
1 answer:
GaryK [48]3 years ago
3 0

Consider all parabolas:

1.

y = x^2 + 6x + 8,\\y=x^2+6x+9-9+8,\\y=(x^2+6x+9)-1,\\y=(x+3)^2-1.

When x=-3, y=-1, then the point (-3,-1) is vertex of this first parabola.

2.

y = 2x^2 + 16x + 28=2(x^2+8x+14),\\y=2(x^2+8x+16-16+14),\\y=2((x^2+8x+16)-16+14),\\y=2((x+4)^2-2)=2(x+4)^2-4.

When x=-4, y=-4, then the point (-4,-4) is vertex of this second parabola.

3.

y =-x^2 + 5x + 14=-(x^2-5x-14),\\y=-(x^2-5x+\dfrac{25}{4}-\dfrac{25}{4}-14),\\y=-((x^2-5x+\dfrac{25}{4})-\dfrac{25}{4}-14),\\y=-((x-\dfrac{5}{2})^2-\dfrac{81}{4})=-(x-\dfrac{5}{2})^2+\dfrac{81}{4}.

When x=2.5, y=20.25, then the point (2.5,20.25) is vertex of this third parabola.

4.

y =-x^2 + 7x + 7=-(x^2-7x-7),\\y=-(x^2-7x+\dfrac{49}{4}-\dfrac{49}{4}-7),\\y=-((x^2-7x+\dfrac{49}{4})-\dfrac{49}{4}-7),\\y=-((x-\dfrac{7}{2})^2-\dfrac{77}{4})=-(x-\dfrac{7}{2})^2+\dfrac{77}{4}.

When x=3.5, y=19.25, then the point (3.5,19.25) is vertex of this fourth parabola.

5.

y =2x^2 + 7x +5=2(x^2+\dfrac{7}{2}x+\dfrac{5}{2}),\\y=2(x^2+\dfrac{7}{2}x+\dfrac{49}{16}-\dfrac{49}{16}+\dfrac{5}{2}),\\y=2((x^2+\dfrac{7}{2}x+\dfrac{49}{16})-\dfrac{49}{16}+\dfrac{5}{2}),\\y=2((x+\dfrac{7}{4})^2-\dfrac{9}{16})=2(x+\dfrac{7}{4})^2-\dfrac{9}{8}.

When x=-1.75, y=-1.125, then the point (-1.75,-1.125) is vertex of this fifth parabola.

6.

y =-2x^2 + 8x +5=-2(x^2-4x-\dfrac{5}{2}),\\y=-2(x^2-4x+4-4-\dfrac{5}{2}),\\y=-2((x^2-4x+4)-4-\dfrac{5}{2}),\\y=-2((x-2)^2-\dfrac{13}{2})=-2(x-2)^2+13.

When x=2, y=13, then the point (2,13) is vertex of this sixth parabola.

You might be interested in
Does anyone know whoever answers i’ll mark brainlist
-Dominant- [34]

Answer:

(1,2)

Step-by-step explanation:

The solution to the system is where the two lines cross.

They cross at x=1 and y=2

(1,2)

8 0
2 years ago
What value of x is in the solution set of 2x – 3 > 11 – 5x?
pochemuha

Given:

2x -3 > 11 -5x

Simplify both sides:

2x - 3 > -5x + 11

Add 5x to both sides:

2x - 3 +5x > -5x + 11 +5

7x - 3 > 11

Add 3 to both sides:

7x - 3 +3 > 11 + 3

7x > 14

Divided 7 to both sides:

\frac{7x}{7} > \frac{14}{7}

x > 2

4 0
3 years ago
Which inequality represents the phrase "paid more than $2.00"?
Nastasia [14]
Is greater than or equal to $.00
6 0
2 years ago
Plz help me I need to know ,What was the towns population in 2005?
Brut [27]
The answer is B: 4,968
5 0
3 years ago
Read 2 more answers
Which statements about the pattern are true?
skelet666 [1.2K]
All the correct answers are C and D.
8 0
3 years ago
Read 2 more answers
Other questions:
  • Find the circumference of a circle inscribed in an equilateral triangle with a side of 9 inches.
    13·1 answer
  • The circumference of a pool is 47 feet. Which formula can you use if you know that C =2 pie r
    10·1 answer
  • I need help please and thank you
    15·1 answer
  • $3.25 marked up by 30% how do i work it out
    10·2 answers
  • Graph the inequality y>-5x+3
    14·1 answer
  • Directions: Identify the slope and y intercept. Then write an equation in y = mx + b form. 11) 40 2 1 r 0 -4 -3 -2 +1 0 1 2 3 -1
    15·1 answer
  • PLEASE HELP ASAP MATH QUIZE Cone B has a volume of 157 cubic in. Cone B is dilated by a factor of 2/3 to create Cone A. What is
    11·1 answer
  • A cable television company offers two different pricing plans. Plan A charges $11.25 per month plus a one time installation fee
    5·1 answer
  • Can someone help me with 15 and 16 Please!
    11·1 answer
  • Use the given numbers above the table in multiplying integers and to fill in the blanks inside the box​
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!