Given h of x equals negative 2 times the square root of x minus 3 end root, which of the following statements describes h(x)?
1 answer:
Answer:
The function h(x) is decreasing on the interval (3, ∞).
Step-by-step explanation:
Please take a look at the attached image.
You will see a graph of the given function h(x) = -2. The function is decreasing.
The function starts at 3 and starts to go towards negative infinity on the x-axis. Therefore the function is decreasing on the interval (3, ∞).
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The sketch of the parabola is attached below
We have the focus
The point
The directrix, c at
The steps to find the equation of the parabola are as follows
Step 1
Find the distance between the focus and the point P using Pythagoras. We have two coordinates;
and 
.
We need the vertical and horizontal distances to find the hypotenuse (the diagram is shown in the second diagram).
The distance between the focus and point P is given by
Step 2
Find the distance between the point P to the directrix
. It is a vertical distance between y and c, expressed as 
Step 3
The equation of parabola is then given as
=
⇒ substituting a, b and c
⇒Rearranging and making 
the subject gives
We have the focus
The point
The directrix, c at
The steps to find the equation of the parabola are as follows
Step 1
Find the distance between the focus and the point P using Pythagoras. We have two coordinates;
We need the vertical and horizontal distances to find the hypotenuse (the diagram is shown in the second diagram).
The distance between the focus and point P is given by
Step 2
Find the distance between the point P to the directrix
Step 3
The equation of parabola is then given as