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

Factor as the product of two binomials <br> X^2 +8x +12 = ?

aksik [14]

The answer to this is (x+6)(x+2)

4 0

3 years ago

Don opened a checking account. Let F represent the

Law Incorporation [45]

Answer:

B and E

Step-by-step explanation:

In the function f(m)= -50m+300

-50 is the gradient meaning it is the rate of change per month. This means that the rate of change is -50 since this is the coefficient of m.

Also, -50m must be negative since m represents a month and you cant have negative months, so you know that the amount of money is decreasing

6 0

3 years ago