Conic Sections — Quiz

Question 8 • Precalculus

The equation negative 1 half times open paren x plus 1 close paren is equal to open paren y minus 5 close paren squared is represented by which graph?

Answer

Image with description On a coordinate plane, a parabola opens to the left. It goes through (negative 9, 7), has a vertex at (negative 1, 5), and goes through (negative 9, 3).

Image with description On a coordinate plane, a parabola opens to the left. It goes through (negative 7, negative 3), has a vertex at (1, negative 5), and goes through (negative 7, negative 7).

Image with description On a coordinate plane, a parabola opens to the right. It goes through (9, negative 3), has a vertex at (1, negative 5), and goes through (9, negative 7).

Image with description On a coordinate plane, a parabola opens to the right. It goes through (7, 7), has a vertex at (negative 1, 5), and goes through (7, 3).

Explanation

Rewrite the equation as (y − 5)² = −½(x + 1), which matches the horizontal-parabola form (y − k)² = 4p(x − h). Its vertex is (h, k) = (−1, 5), and since 4p = −½ is negative, it opens left. For example, when y = 7 or y = 3, the equation gives x = −9, matching the points in choice A.

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