What’s is part A?? .

A. 3

B. 4

C. 1

D. 2

Step-by-step explanation:

Consider all equations:

A.

This is the equation of parabola with vertex at point

The y-intercept is at point

Since

,

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.

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.

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.

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.

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

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

the answer is; biodiversity resulting from few ancestors

adaptive radiation occurs when a population is subjected to a large natural environment with spatial ecological variations. the parts of the population in the different ecologies begin to adapt to their local environments. due to non-random mating across the large populations, this causes the different populations from the large population to speciate within their local environments. they, therefore, diverge to different species sharing a common ancestor.  

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step-by-step explanation: