The equation of a direct variation is of the form
But the given function can be rewritten as
This is a partial variation,
is the constant of variation and
is the fixed constant.
You can rewrite the equation in vertex form to find some of the parameters of interest.
x² +8x +4 = -4y
x² +8x +16 -12 = -4y
(x+4)² -12 = -4y
y = (-1/4)(x +4)² +3
From this, we see
the vertex is (-4, 3).
The scale factor, (-1/4) is 1/(4p), where p is the distance from the vertex to the focus. Solving for p, we have
-1/4 = 1/(4p)
p = -1 . . . . . multiply by -4p
So, the focus is 1 unit below the vertex.
The focus is (-4, 2).
The directrix is the same distance from the vertex, but in the opposite direction, hence
the directrix is y = 4.
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On a graph, if all you know is the vertex, you can draw a line with slope 1/2 through the vertex. It intersects the parabola at the y-value of the focus. Then the distance from that point of intersection to the axis of symmetry (where the focus lies) is the same as the distance from that point to the directrix.
Every point on the parabola, including the vertex and the point of intersection just described, is the same distance from the focus and the directrix. This point of intersection is on a horizontal line through the focus, so finding the distance is made easy.
Answer: any set of the choices given can make a triangle.
The shapes and sizes will be different, of course. None of the sets given will produce a Right Triangle.
Step-by-step explanation:
Answer:
-5 is in the negatives, and 3 is positive, therefore greater than -5 three is greater than -5
Hey, I think an image is needed to answer this question.
