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Mathematics

1 answer:

olga2289 [7]3 years ago

5 0

Answer: a) degree and sign

b) end behavior: left side → +∞, right side → -∞

c) x-intercepts: x = -1.3, 0.3, 1.0

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

end behavior can be determined by two things:

1) the degree of the polynomial:

if the degree is an even number, then the end behavior will be the same for both the left and right sides.
if the degree is an odd number, then the end behavior will be different for both the left and right sides.

2) the sign of the leading coefficient:

If the leading coefficient is positive, then the end behavior of the right side goes to positive infinity
If the leading coefficient is negative, then the end behavior of the right side goes to negative infinity

W(x) = -5x³ + 7x - 2

Degree: 3 (odd)

Leading Coefficient: negative

So, end behavior is: right side goes to negative infinity, right side goes to positive infinity.

See attachment for x-intercepts. <em>I set the x-axis to represent tenths </em>

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A radio telescope has a parabolic surface, as shown below.If the telescope is 1 m deep and 8 m wide, how far is the focus from t

scoray [572]

Answer:

4 m

Step-by-step explanation:

The equation can be written ...

y = (x/4)² = (1/16)x²

where the divisor 4 is the horizontal scale factor that makes the parabola 8 m wide at y = 1 m.

This can also be written as ...

y = 1/(4p)x² = (1/16)x²

from which we can see ...

4p = 16

p = 4

In this form, p is the distance from the vertex to the focus, 4 meters.

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Another way to find the y-coordinate of the focus is to draw a line with slope 1/2 through the vertex. It will intersect the parabola at the point where the vertical distance to the directrix is the same as the horizontal distance to the focus. The y-coordinate of that point is the y-coordinate of the focus.