3 years ago

Find the domain and range of the relation:

Mathematics

1 answer:

Novay_Z [31]3 years ago

6 0

Answer:

I am not getting what is this

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What is the focus of the parabola? y=−1/4x2−x+3

alex41 [277]

Answer: Focus = (-2, 3)

<u>Step-by-step explanation:</u>

$y=-\dfrac{1}{4}x^2-x+3\\\\\rightarrow a=-\dfrac{1}{4},\ b=-1$

First let's find the vertex. We do that by finding the Axis-Of-Symmetry:

$AOS: x=\dfrac{-b}{2a}\quad =\dfrac{-(-1)}{2(\frac{-1}{4})}=\dfrac{1}{-\frac{1}{2}}=-2$

Then finding the maximum by inputting x = -2 into the given equation:

$y=-\dfrac{1}{4}(-2)^2-(-2)+3\\\\y=-1+2+3\\\\y=4$

The vertex is: (-2, 4)

Now let's find p, which is the distance from the vertex to the focus:

$a=\dfrac{1}{4p}\\\\\\-\dfrac{1}{4}=\dfrac{1}{4p}\\\\\\p=-1$

The vertex is (-2, 4) and p = -1

The focus is (-2, 4 + p) = (-2, 4 - 1) = (-2, 3)

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3 years ago

the coordinates of the endpoints of line AB and line CD are A(x1, y1), B(x2, y2), C(X3,Y3), and D(x4, y4). which condition prove

pogonyaev

Find the slope for the two lines and state that they are equal (condition for parallel lines)

Slope of line AB

[y2 - y1] / [x2 - x1]

Slope of line CD

[y4 - y3] / [x4 - x3]

Condition

[y2 - y1] / [x2 - x1] = [y4 - y3] / [x4 - x3]

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