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
Eddi Din [679]
3 years ago
8

Describe the graph that would be used to solve the equation –x2 + 4 = x + 2 using a system of equations. How will you use the gr

aph to find the solution(s)?

Mathematics
2 answers:
babymother [125]3 years ago
5 0

Answer:

The graph consists of a parabola and a line. The parabola opens down and has a vertex of (0, 4). The line has a slope of 1 and a y-intercept of 2

c:

gayaneshka [121]3 years ago
3 0

Answer:

The solutions are (-2 , 0) and (1 , 3)

Step-by-step explanation:

∵ -x² + 4 = x + 2

* y = -x² + 4 ⇒ is quadratic represented by parabola

 The parabola open downward because coefficient of x² is negative

 The x-coordinate of its vertex = -b/2a, where b is the

  coefficient of x and a is the coefficient of x²

∴ x = 0/2(-1) = 0

∴ The y-coordinate of the vertex = (0)² + 4 = 4

∴ The maximum point of the parabola is (0 , 4)

∵ -x² + 4 intersects x-axis at y = 0

∴ -x² + 4 = 0 ⇒ -x² = -4 ⇒ x² = 4

∵ x² = 4

∴ x = ±√4 = ± 2

∴ the parabola intersects x-axis at -2 , 2

∵ y = x + 2 represented by a line its slope = 1

  It intersects y-axis at 2

∵ x + 2 intersects x-axis at y = 0

∴ x + 2 = 0

∴ x = -2

∴ The parabola and the line intersect each other at

  x = -2 and y = 0

To find all the point of intersection between the 2 equations we will solve them as a system of equations

∵ y= -x² + 4  and y = x + 2

∴ -x² + 4 = x + 2

∴ -x² + 4 - x - 2 = 0

∴ -x² - x + 2 = 0 ⇒ × -1

∴ x² + x - 2 = 0 ⇒ factorize

∴ (x + 2)(x - 1) = 0

∴ x + 2 = 0 ⇒ x = -2

∴ x - 1 = 0 ⇒ x = 1

* when x = -2 ⇒ y = -2 + 2 = 0 ⇒ (-2 , 0)

* when x = 1 ⇒ y = 1 + 2 = 3 ⇒ (1 , 3)

The solution graphically

You might be interested in
What is the value of x in the equation 8x-2y=48, when y=4
Oksanka [162]
8x - 2y = 48,  y =4

8x - 2(4) = 48
8x - 8 = 48
8x = 48+8
8x  = 56
x = 56/8 = 7

x = 7
8 0
3 years ago
Read 2 more answers
How do you plot a fraction on a graph that only allows whole numbers?
klio [65]

Answer:

Depends, rise over run could be considered a fraction, or if it's a number that has a whole number like one and 3/4 then you just plot the point to the best of your ability. In other words guess.

8 0
2 years ago
Read 2 more answers
Can someone please explain to me how to tell if a number it's prime or not
slavikrds [6]

Answer:

A prime number is a number that can only be divided by 1 and itself.

3 0
3 years ago
Read 2 more answers
HELP!!!! <br><br> -5 3/4 - 3 1/2 = ?
umka21 [38]

Answer:

9.25 or 9 1/4

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Last one guys I promise lol. btw helpp
Marianna [84]
63 dollars 3 hours

21 dollars 1 hour
8 0
3 years ago
Other questions:
  • The state of Colorado is in the shape of a rectangle whose length is 380 miles and whose length is 380 miles and whose width is
    11·2 answers
  • Parker has $10 to spend at Dale's Market.He orders 1/2 pound of Swordfish and 1 1/4 pounds of Grouper.How much will Parker have
    8·1 answer
  • HOW DO I FIND THE SQUARE ROOT OF A NUMBER !?!?!?!?!<br><br> TXT ME TOO
    15·2 answers
  • X^2-18x+67=0 Solve the quadratic equation by completing the square.
    8·1 answer
  • Why are the people who delete questions such A H O L E S
    9·1 answer
  • Six cakes cost £1.80 how much do ten cakes cost
    9·2 answers
  • Neda sells televisions. She earns a fixed amount for each television and an additional $15 if
    11·1 answer
  • Which graph represents a function?
    11·1 answer
  • You are offered two summer jobs. The first job pays $20 for each day of work. The second
    13·1 answer
  • Find x (btw if you answer randomly to just get point imma report ur acc)​
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!