171039
AssignmentMultiple Select

Conic Inequalities

Question 171039 • Precalculus

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 is (2, –1).

Answer
A
Because only the y quantity is squared, the curve is a parabola.
B
The parabola opens right because 6 is in front of the x-quantity.
C
There is a strict inequality so the boundary is included in the solution set.
D
The shading is outside the parabola because (0, 0) satisfies the inequality.
E
The values subtracted from x and y in the equation are the coordinates of the vertex which is (2, –1).

Explanation

The boundary equation, (y + 1)² = 6(x − 2), is a parabola because only y is squared. In the form (y − k)² = 4p(x − h), the positive coefficient 6 means it opens right, and its vertex is (h, k) = (2, −1). The strict inequality excludes the boundary, so C is false. Testing (0, 0) gives 1 > −12, which is true; the origin lies on the outside (left) side of this right-opening parabola, so that side is shaded.

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