Which of the following statements are true of the parabola shown?
1. It has a directrix of x = -4.
2. It opens to the left.
3. It has a vertex at the origin.
4. The axis of symmetry is the y-axis.
5. It has a focus at (4, 0).

True statements are:

Step-by-step explanation:

We have the following statements to check on whether it's right or wrong:

1. It has a directrix of x = -4:

According to figure , parabola directrix is at -4 i.e. at x = -4 , Therefore this statement is true!

2. It opens to the left:

In figure, Parabola opens to right not left , Therefore this statement is wrong!

3. It has a vertex at the origin:

Vertex of Parabola is at what points not shown in figure. Therefore this statement cannot be confirmed as true.

4. The axis of symmetry is the y-axis:

Axis of symmetry for above parabola is x-axis as it cuts parabola into two equal halves , y-axis doesn't do this ! Therefore this statement is wrong!

5. It has a focus at (4, 0):

Parabola focus is at on x-axis . And so, Therefore this statement is true!

is this a multiple choice question?

if so it's a and c

(x, y)→(x − 8, y − 7)

step-by-step explanation:

enjoy!