Miranda graphed (y + 1)2 > 6(x - 2). Which could Miranda use to justify that her graph is correct? Check all that apply.
Because only the y quantity is squared, the curve is a parabola.
The parabola opens right because 6 is in front of the x-quantity.
There is a strict inequality so the boundary is included in the solution set.
The shading is outside the parabola because (0,0) satisfies the inequality.
The values subtracted from x and y in the equation are the coordinates of the vertex which
O O O O

The correct options that describe the inequality (y + 1)² > 6·(x - 2)

1) Because only the 'y' quantity is squared the curve is a parabola

2) The parabola opens right because 6 is in front of the 'x' quantity

3) The shading area is outside the parabola because (0, 0) satisfies the inequality

4) The values subtracted from 'x', and 'y' in the equation are the coordinates of the vertex

Step-by-step explanation:

The given inequality graphed by Miranda is presented as follows;

(y + 1)² > 6·(x - 2)

By simplification, we get;

Given that the inequality is of the form (y - k)² > 4·p·(x - h), we have;

The curve is a parabola as only the 'y' quantity is squared

-k = 1

∴ k = -1

4·p = 6

∴ p = 6/4 = 3/2 = 1.5

p = 1.5

-h = -2

∴ h = 2

The vertex of the parabola = (h, k) = (2, -1)

The axis of symmetry = The x-axis

p = 1.5 > 0, therefore, the parabola opens right

Therefore, the parabola opens right because 6 is in front of the 'x' quantity

There is a strict inequality therefore the boundary is not included in the solution set

When x = 0 and y = 0, we have;

(y + 1)² > 6·(x - 2)

(0 + 1)² > 6·(0 - 2)

1² > 6 × (-2)

1 > -12, which satisfies the inequality and (0, 0) is on the left and below the vertex, therefore, the shaded area is outside the parabola

The vertex of the parabola given in the form, (y - k)² > 4·p·(x - h), is (h, k), which are the values subtracted from 'x', and 'y' in the equation

Therefore, the vertex of the given parabola, (y + 1)² > 6·(x - 2) = (2, -1)

Because only the y quantity is squared, the curve is a parabola.

The parabola opens right because 6 is in front of the x-quantity.

The shading is outside the parabola because (0,0) satisfies the inequality.

The values subtracted from x and y in the equation are the coordinates of the vertex which

Step-by-step explanation:

edge 2021

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

b

step-by-step explanation: