Question

Identify the directrix, focus, and vertex of the parabola in the figure.

A parabola goes through (negative 3, 3) & (1, negative 1). A point is below the parabola at (negative 3, 2). A line above the parabola goes through (negative 3, 4) & (0, 4).

© 2019 StrongMind. Created using GeoGebra.

Match the correct coordinates or equation with the correct part of the parabola.

Answer 1

The directrix, focus, and vertex of the parabola are y = 4, (-1, 2) and (-1, 1), respectively

Identifying the directrix, focus, and vertex of the parabola

From the question, we have the following parameters that can be used in our computation:

• Points = (-3, 3) & (1, -1).
• Point below the parabola = (-3, 2).
• Line above the parabola = (-3, 4) & (0, 4)

The vertex is the midpoint of the line connecting the focus and the directrix.

So, we have the vertex to be

(h, k) = (-3 + 1, 3 - 1)/2

(h, k) = (-1, 1)

Since the point (-3, 2) is below the parabola and lies on the axis of symmetry, the distance from the vertex to the focus is 1 unit (from the vertex to the point (−3, 2)).

So, we have the focus to be

Focus = (-1, 1 + 1)

Focus = (-1, 2)

The directrix is a horizontal line that is symmetrically opposite to the focus with respect to the vertex.

Since the given line above the parabola passes through (-3, 4) and (0, 4), the directrix is the horizontal line y = 4