A parabola is the locus of a point such that the distance from a fixed line called directrix and the distance from a fixed point called focus is constant.

The equation of a parabola with a vertex at (h, k) with axis of symmetry parallel to the y axis is given as:

$4p(y-k)=(x-h)^2$

The directrix is at y = k - p, and focus is at (h, k + p).

Given an equation -1/16(x-3)^2 + 4 = y, expressing it in standard form is:

$-\frac{1}{16}(x-3)^2+4=y\\\\(y-4)= -\frac{1}{16}(x-3)^2\\\\-16(y-4)=(x-3)^2\\\\$

Comparing with the standard form:

The center = (h, k) = (3, 4)

Also, -16 = 4p

p = -4

Directrix is at y = k - p = 4 - (-4) = 8

Directrix is at y = 8

The focus is at (h, k + p) = (3, 4 + (-4)) = (3, 0)

The focus is at (3, 0)

3 0

3 years ago

A sled dog racer completed a race in 6 hours. Because of changes in the terrain, his average speed for the last 48 miles was twi

Serga [27]

A sled dog racer completed a race in 6 hours. Because of changes in the terrain, his average speed for the last 48 miles was twice as fast as his average speed for the first 12 miles. Which equation can be used to find r, his average speed in miles per hour, during the first 12 miles?

4 0

3 years ago

Write an<br> inequality to compare – 24 and -14.

Anit [1.1K]

Answer: The position of -24 is to the left of -14.

The position of -14 is to the right of -24.

Step-by-step explanation:

We can conclude that -18 < -2.

We can conclude that -14> -24.

3 0

3 years ago