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
Lisa [10]
3 years ago
7

What’s is part A?? .....

Mathematics
2 answers:
bixtya [17]3 years ago
4 0

Answer:

A. 3

B. 4

C. 1

D. 2

Step-by-step explanation:

Consider all equations:

A. y=x^2 -6x+8

This is the equation of parabola with vertex at point

x_v=\dfrac{-b}{2a}=\dfrac{-(-6)}{2\cdot 1}=3\\ \\y_v=3^2-6\cdot 3+8=9-18+8=-1

The y-intercept is at point

x=0\\ \\y=0^2-6\cdot 0+8=8

Since

x^2 -6x+8=x^2-4x-2x+8=x(x-4)-2(x-4)=(x-2)(x-4),

the x-intercepts are at points (2,0) and (4,0)

The leading coefficient is 1 > 0, then the parabola opens upwards.

Hence, the graph of this parabola is 3.

B. y=(x-6)(x+8)

This parabola has two x-intercepts at points (6,0) and (-8,0).

The leading coefficient is 1 > 0, then the parabola opens upwards.

The only possible choice is parabola 4.

C. y=(x-6)^2+8

This parabola has the vertex at point (6,8), opens upwards, therefore does not intersect the x-axis.

The graph of this parabola is 1.

D. y=-(x+8)(x-6)

This parabola has two x-intercepts at points (6,0) and (-8,0).

The leading coefficient is -1 > 0, then the parabola opens downwards.

The only possible choice is parabola 2.

fredd [130]3 years ago
4 0

Answer:

Equation A matches Graph 3, because the parabola is opened upward and intersected the x-axis at points (2 , 0) and (4 , 0)

Equation B matches Graph 4, because the parabola is opened upward,  intersected the x-axis at point (-8 , 0) , (6 , 0) and the y-axis at point (0 , -48)

Equation C matches Graph 1, because the parabola is above the x-axis

Equation D matches Graph 2, because the parabola is opened downward

Step-by-step explanation:

The quadratic function f(x) = ax² + bx + c is represented graphically by a parabola which has a vertex point (h , k)

The vertex form of the quadratic function is f(x) = (x - h)² + k

  • The parabola is opened upward if a is positive or downward if a is negative
  • The parabola intersected the y-axis at c
  • The parabola intersected the x-axis at the zeroes of the function
  • If k the y-coordinate of the vertex of the parabola is greater than 0, then the parabola never intersects the x-axis

Equation A

∵ y = x² - 6x + 8

∵ a = 1

- By using the 1st note above

∴ The graph of the equation is a parabola opened upward

- Lets find its zeros (Put y = 0)

∵ x² - 6x + 8 = 0

- Factorize it into two factors

∴ (x - 2)(x - 4) = 0

- Equate each factor by 0

∵ x - 2 = 0 ⇒ add 2 to both sides

∴ x = 2

∵ x - 4 = 0 ⇒ add 4 to both sides

∴ x = 4

∴ Its zeroes are 2 and 4

- That means the parabola intersects the x-axis at 2 and 4

∴ The graph of equation A is figure 3

Equation A matches Graph 3, because the parabola is opened upward and intersected the x-axis at points (2 , 0) and (4 , 0)

Equation B

∵ y = (x - 6)(x + 8)

- Equate each factor by 0

∵ x - 6 = 0 ⇒ add 6 to both sides

∴ x = 6

∵ x + 8 = 0 ⇒ subtract 8 from both sides

∴ x = -8

∴ Its zeroes are 2 and 4

- That means the parabola intersects the x-axis at points (-8 , 0)

    and (6 , 0)

∵ (x - 6)(x + 8) = x² + 8x - 6x - 48

- Add like terms

∴ (x - 6)(x + 8) = x² + 2x - 48

∴ y = x² + 2x - 48

- Find the value of a and c

∴ a = 1 and c = -48

∵ a is positive

∴ The parabola is opened upward

∵ c = -48

∴ The parabola intersects the y-axis at point (0 , -48)

∴ The graph of equation B is figure 4

Equation B matches Graph 4, because the parabola is opened upward intersected the x-axis at point (-8 , 0) , (6 , 0) and the y-axis at point (0 , -48)

Equation C

∵ y = (x - 6)² + 8

- The equation is in the vertex form

∴ The coordinates of the vertex point are h = 6 and k = 8

∴ The vertex of the parabola is (6 , 8)

- By using the 4th note above

∵ k > 0

∴ The parabola does not intersect the x-axis

∴ the parabola is above the x-axis

∴ The graph of equation C is figure 1

Equation C matches Graph 1, because the parabola is above the x-axis

Equation D

∵ y = -(x + 8)(x - 6)

(x + 8)(x - 6) = x² - 6x + 8x - 48

- Add like terms

∴ -(x - 6)(x + 8) = -(x² + 2x - 48)

- Multiply each term by (-)

∴ -(x - 6)(x + 8) = - x² - 2x + 48

∴ y = -x² - 2x + 48

- Find the value of a

∴ a = -1

- Use the 1st rule above

∵ a < 0

∴ The parabola is opened downward

∴ The graph of equation D is figure 2

Equation D matches Graph 2, because the parabola is opened downward

You might be interested in
Express (25 1/2) ^3 in simplest radical form
Mkey [24]

Step-by-step explanation:

i think this is the answer if it's wrong I'm sorry

5 0
2 years ago
Is 1/8 bigger or smaller than 3/4?
Advocard [28]
Small, because 1 divided by 8 = 0.125, and 3 divided by 4 = .75 Hope this helps!
5 0
3 years ago
Read 2 more answers
Please help! If possible please show your work. Thank you in advance!! :D
Rudiy27

Answer:

  • (-4)³ = -64
  • -64

Step-by-step explanation:

The first step in solving the equation is to cube both sides:

  (∛x)³ = (-4)³ . . . . . = (-4)(-4)(-4) = 16(-4) = -64

  x = -64 . . . . . simplified

__

We're not sure what "checking" is supposed to involve here. Usually, one would check the answer by seeing if a true statement is made when the answer is put into the original equation.

  ∛(-64) = -4 . . . true

Many calculators will not compute √(-64) because they compute roots using logarithms. The log of a negative number is not defined.

So, the way one would check this is to cube both sides, which is how we got the answer in the first place. We expect the same result from doing the same operation again, so it isn't really a check.

6 0
2 years ago
Matt claims that 1/3 can indicate a point on a number line as well as distance. Is he correct? Explain.
inna [77]
Yes he is correct because 1/3 can be shown on a number line
5 0
3 years ago
Read 2 more answers
Set up an linear equation and solve the following number word problem:
IRINA_888 [86]

Answer:

let the number be y

4(y-7)=48

y-7=48/4

y-7=12

y=12+7=19

I would appreciate if my answer is chosen as a brainliest answer

3 0
2 years ago
Other questions:
  • For which of the values of a and b is the following statement not true?
    5·1 answer
  • What is 4(0.5x + 2.5y - 0.7y - 1.3y + 4) simplified?
    14·1 answer
  • What does 204 thousands equal
    12·1 answer
  • Kia stuffs 228 envelopes in an hour. What is the average number of envelopes Kia stuffs per minute?
    12·1 answer
  • Cindy plans to shop for her school supplies and wants to know how much money she would need to spend. from her friend she knows
    7·1 answer
  • Which measurement is most accurate to describe the amount that a teacup can hold? 6 fl. oz. 2 cups 1 pint 1.5 quarts
    7·2 answers
  • Write an expression that shows “the product of 3 and the sum of 6 and 8.”
    10·1 answer
  • Evaluate the following expression.<br><br> 2⁵ + (10 - 7)⁴ + 6
    12·2 answers
  • (Drop downs:) 8,6,5.5<br> (Drop downs 2:) 10.5,8,5.5 <br> (Drop downs 3:) 33,22,11
    10·1 answer
  • PLSSS I NEED THE ANSWER
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!