The functions f(x) and g(x) are shown on the graph.

Mathematics

1 answer:

goldfiish [28.3K]2 years ago

7 0

Answer:Soo really I could give a fucif u believe me or not but the answer is d

Step-by-step explanation:

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If f(x)= 2x2+1 what is f(x) when x=3?

omeli [17]

The correct answer is 13

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3 years ago

Find two numbers which have a sum of 132 and that can be written as the simplified<br> ratio 3:8

Molodets [167]

Answer:

96 and 36

Step-by-step explanation:

3+8 = 11

132/11 = 12

so:

12 x 3 = 36

12 x 8 = 96

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2 years ago

Find the standard form of the equation of the parabola with a focus at (0, 8) and a directrix at y = -8

Gekata [30.6K]

First, let $(x,y)$ be a point in our parabola. Since we know that the focus of our parabola is the point (0,8), we are going to use the distance formula to find the distance between the two points:
$\sqrt{(x-0)^{2}+(y-8)^{2}}$

Next, we are going to find the distance between the directrix and the point in our parabola. Remember that the distance between a point (x,y) of a parabola and its directrix, $y=c$ , is: $|y-c|$ . Since our directrix is y=-8, the distance to our point will be:
$|y-(-8)|$
$|y+8|$

Now, we are going to equate those two distances, and square them to get rid of the square root and the absolute value:
$\sqrt{(x-0)^{2}+(y-8)^{2}}=|y+8|$
$(\sqrt{(x-0)^{2}+(y-8)^{2}})^{2}=|y+8|^{2}$
$(x-0)^{2}+(y-8)^{2}=y+8$

Finally, we can expand and solve for $y$ :
$x^2+y^2-16y+64=y^2+16y+64$
$x^{2}-16y=16y$
$32y=x^{2}$
$y= \frac{1}{32} x^2$

We can conclude that t<span>he standard form of the equation of the parabola with a focus at (0, 8) and a directrix at y = -8 is </span> $y= \frac{1}{32} x^{2}$