Question

the following graph shows a parabola with symmetric points at (-7,1) and (-7,-3). the focus is the point (-5,-1) and the directrix is x = -2. the vertex is the point (-3,-1) and the axis of symmetry is the line where y = -1. true or false. these attributes are calculated correctly for this parabola. possible points: 5 10/3 dg 3-2: quadratic attributes

Explanation:

Step1: Recall parabola properties

For a parabola, the axis of symmetry passes through the vertex. If the axis of symmetry is $y = - 1$, the $y$-coordinate of the vertex is - 1. The focus and directrix are equidistant from the vertex along the axis perpendicular to the axis of symmetry.

Step2: Analyze given points

The focus is $(-5,-1)$. If the directrix is $x = 2$, the vertex should be the mid - point between the focus and the point on the directrix with the same $y$-coordinate. The mid - point of $x=-5$ (focus $x$-coordinate) and $x = 2$ (directrix $x$-coordinate) is $\frac{-5 + 2}{2}=-\frac{3}{2}$, so the vertex should be $(-\frac{3}{2},-1)$. Also, symmetric points on a parabola with respect to the axis of symmetry have the same $y$-coordinate. Given symmetric points $(-7,1)$ and $(-7, - 3)$ have different $y$-coordinates which is incorrect for a parabola symmetric about $y=-1$. So the attributes are not calculated correctly.

Answer:

False