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2 years ago

Find the standard form of the equation of the parabola with a focus at (-2, 0) and a directrix at x = 2.

1 answer:

4 0

Standard form is, hold a sec

x=2 is directix
that means it opens left or right
so we must use
(y-k)²=4p(x-h)
where vertex is (h,k) and p is distance from focus to vertex
also shortest distance from vertex to directix
the shortest distance from focus to directix is 2p
if p>0 then the parabola opens right
if p<0 then pareabola opens left

so
(-2,0) and x=2
the distance is 4
4/2=2
p=2
wait, positive or negative
focus is to the left of the directix so p is negative
p=-2

vertex is 2 to the right of the focus and 2 to the left of directix
vertex is (0,0)

so
(y-0)²=4(-2)(x-0) or
y²=-8x is da equation
not sure what form is standard tho

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HELPP HELP. It’s about slope!!!! Explanation needed

OleMash [197]

Answer:

x = -3

Step-by-step explanation:

A line has equation: y = ax + b

This line has slope a = 1

This line passes (4, 1)

=> 1 = 4 + b

=> b = -3

=> The equation of this line : y = x - 3

This line passes another point (x, -6)

=> -6 = x - 3

=> x = -6 + 3

=> x = -3

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3 years ago

What is the slope of the line through (-9, 6) and (-3, 9)? Choose 1 answer:

trasher [3.6K]

Given: Points (-9, 6) and (-3, 9)

Find: The slope of the line that goes through those two points

Solution: In order to find the slope of the line that goes through the points that were provided we have to use the slope formula. This formula subtracts the y-coordinates from each other and also the x-coordinates from each other to determine the rise/run which would give us the rate of change.

Plug in the values

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{9 - 6}{-3 - (-9)}$

Simplify the expression

$m = \frac{3}{-3 + 9}$

$m = \frac{3}{6}$

$m = \frac{1}{2}$

Therefore, looking at the given options we can see that the best fitting one would be option A, 1/2.

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1 year ago

Read 2 more answers

How do I simplify the n^-6*n^3 topic "Negative and Zero Exponents"

Alchen [17]

Since you’re multiplying n^-6 and n^3, you can add the exponents: -6+3 = -3

n^-6 * n^3 = n^-3

If you need to finish without having a negative exponent in your answer, then remember a negative exponent means that factor is on the wrong side of the fraction.

n^-3 = n^-3 / 1 = 1/n^3

when the factor moves to the other side of the fraction, the side of the exponent changes.

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2 years ago

the perimeter of a triangle is 38 ft . One side is 14 ft long . Another side is 9 ft long . How long is the third side ?

Aleks [24]

38 - (14+9) = 15ft long

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3 years ago

Which of the following functions is graphed below.

Valentin [98]

Answer: Option A

$y=\left \{ {{x^2 +2;\ \ x$

Step-by-step explanation:

In the graph we have a piecewise function composed of a parabola and a line.

The parabola has the vertex in the point (0, 2) and cuts the y-axis in y = 2.

The equation of this parabola is $y = x ^ 2 +2$

Then we have an equation line $y = -x + 2
$

Note that the interval in which the parabola is defined is from -∞ to x = 1. Note that the parabola does not include the point x = 1 because it is marked with an empty circle " о ."

(this is $x< 1$ )

Then the equation of the line goes from x = 1 to ∞ . In this case, the line includes x = 1 because the point at the end of the line is represented by a full circle .

(this is $x\geq 1$ )

Then the function is:

$y=\left \{ {{x^2 +2;\ \ x$

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3 years ago