Question

Find the focus and directrix of the parabola y = 1/2(x+1)2 + 4.
C A) Focus: (1,41/2); Directrix: y = 31/2
C B) Focus: (-1,41/2); Directrix: y= 31/2
C C) Focus: (1,31/2); Directrix: y = 41/2
CD) Focus: (-1,31/2); Directrix: y = 41/2

Answer 1

Answer is B! Correct on exam!

Step-by-step explanation:

1. Identify the values for a, h, and k: a= 1/2 h= -1 k= 4. (Remember that the sign of h changes!)

2. Determine vertex: (-1,4)

3. Determine x and y for focus: X= -1 (same as vertex) y= K + 1/4(a)

Substitute what we know into that formula: y= 4 + 1/4(1/2)

y= 4 + 1/2 so y= 4 1/2.

4. Determine directrix: y= k - 1/4(a) ]

Substitute in what we know: y= 4 - 1/4(1/2)

y= 4-1/2 so y= 3 1/2

Answer 2

The focus and directrix of the parabola are (-1, 9/2) and y=7/2 respectively.

The given function is y = 1/2(x+1)² + 4.

We need to find the focus and directrix of the parabola.

What are focus and directrix?

A parabola is a set of all points in a plane which are an equal distance away from a given point and given line. The point is called the focus of the parabola and the line is called the directrix. The focus lies on the axis of symmetry of the parabola.

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Directrix: Use the vertex form to find the directrix

y=7/2

Focus: Use the vertex form to find the focus.

(-1, 9/2)

Axis of symmetry: x=-1

The coordinates to plot the graph are as follows:

(-3, 6), (-2, 9/2), (-1, 4), (0, 9/2) and (1, 6).

Therefore, the focus and directrix of the parabola are (-1, 9/2) and y=7/2 respectively.

To learn more about the parabola visit:

https://brainly.com/question/21685473.

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