Find the focus and directrix of the parabola y= 1/2 (x+2)^2 - 3 A. The focus is at (–2,–2) and the directrix is at y = –4. B. The focus is at (–2,–3) and the directrix is at y = –5. C. The focus is at (–2,–2 1/2) and the directrix is at y = –3 1/2. D. The focus is at (–2,–1 1/2) and the directrix is at y = –2 1/2.

C. The focus is at and the directrix is at

Step-by-step explanation:

First of all, let us learn about the formula to find Focus and Directrix from the standard equation of a parabola.

Standard form of a parabola is given as:

where the focus is and

the directrix is

Now, we are given the equation of parabola as:

Let us try to convert it to standard form:

Comparing the above with standard equation of parabola :

So, Focus is at

Focus is at .

Equation of directrix:

Also, please refer to the attached image for the diagram of given parabola, focus and directrix.

So, the answer is:

C. The focus is at and the directrix is at

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation:

step-by-step explanation: