I don't think i've been so confused ever, how do I solve this using long division?

Derive the equation of the parabola with a focus at (-2,4) and a directrix of y=6 . Put the equation in standard form

Maru [420]

Answer:

$y = - \frac{1}{4} {(x + 2)}^{2} + 5$

Step-by-step explanation:

The vertex of this parabola is the midpoint of the focus (-2,4) and where the directrix intersects the axis of symmetry of the parabola (-2,6)

This parabola must open downwards due to the position of the directrix and has equation of the form:

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

where (h,k) is the vertex.

This implies that:

$h = - 2$

and

$k = \frac{4 + 6}{2} = 5$

The value of p is the distance from the vertex to the focus:

$p = |6 - 5| = 1$

We substitute all the values into the formula to get:

$(x - - 2)^{2} = - 4(1){(y - 5)}$

${(x + 2)}^{2} = - 4(y - 5)$

Or

$y = - \frac{1}{4} {(x - 5)}^{2} + 5$

4 0

3 years ago

Lucy loves to wear gloves. She has four red gloves and two blue gloves in her drawer. They are not separated into pairs. One dar

rjkz [21]

Matching gloves........

8 0

3 years ago

State the domain, the range, and the intervals on which function is increasing, decreasing, or constant in interval notation

aleksandr82 [10.1K]

Answer:

Domain: $[-1,\infty)$

Range: $(-\infty, 3]$

Decreases over: $(-1,-\infty)$

Step-by-step explanation:

Given

$f(x) = -\sqrt{x + 1} + 3$ --- Missing from the question

Solving (a): The domain

To get the domain, the expression under the square root must not be negative.

In other words:

$x + 1 \ge 0$

Solve for x

$x + 1 -1\ge 0-1$

$x \ge -1$

Hence, the domain is:

$[-1,\infty)$

To get the range, we plot the values of the domain in the expression.

$x = -1$

$f(x) = -\sqrt{x + 1} + 3$

$f(-1) = -\sqrt{-1+1} +3$

$f(-1) = -\sqrt{0} +3$

$f(-1) = -0 +3$

$f(-1) = 3$

$x = \infty$

$f(\infty) = -\sqrt{\infty +1}+3$

$f(\infty) = -\sqrt{\infty}+3$

$f(\infty) = -\infty+3$

$f(\infty) = -\infty$

So, the range is: $(-\infty, 3]$

To get the interval where the function increases or not, we simply plot the graph of f(x).

See attachment for graph.

From the attachment, it will be observed that the graph of f(x) continuously decreases from x = -1, and it never increased.

This implies that, the graph decreases over the interval $(-1,-\infty)$

6 0

3 years ago

Instructions: a) Graph both of the lines (hint: hold shift to draw a straight line) b) state the point of intersection.

Alik [6]

Answer:

there is the ansere

Step-by-step explanation:

the ansere is all doing - 3/4 x-2 is all done.

3 0

3 years ago

HELP ME!!

mihalych1998 [28]

Answer:

cos2∅= -0.557

tan2∅= --1.49

Step-by-step explanation:

Given:

cos∅=-8/17

By trigonometric ratios:

as cos∅=adjacent/hypotenuse

hypotenuse= 17

adjacent=-8

Now finding perpendicular using Pythagoras theorem:

c2=a2+b2

17^2=(-8)^2+b^2

289-64=b^2

b^2=225

b=±15

b=-15 as ∅ is in third quadrant so both the opposite and adjacent sides be in 3rd quadrant

tan∅=opposite/adjacent

tan∅=-15/-8

sin∅=-15/17

Now finding cos2∅

cos2∅= 1-2sin^2∅

=1 - 2(-15/17)^2

=1 -450/289

= -161/289

=-0.557

finding tan2∅

tan2∅= 2tan∅/1-tan^2∅

= 2(-15/-8) / 1-(-15/-8)^2

= (15/4) / 1-225/64

=(15/4) / (-161/64)

= -240/161

=-1.49 !

6 0

3 years ago