The graph shows a parabola and its focus. Write the equation of the parabola in vertex form.

Mathematics

1 answer:

finlep [7]3 years ago

7 0

9514 1404 393

Answer:

y = -1/12x² +2

Step-by-step explanation:

For vertex (h, k) and vertex-to-focus distance p, the vertex form equation is ...

$y=\dfrac{1}{4p}(x-h)^2+k$

Here, the vertex-to-focus distance is -1-2 = -3 units. The vertex is (h, k) = (0, 2). So, the equation of the parabola is ...

$\boxed{y=-\dfrac{1}{12}x^2+2}$

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I need help finding the y-intercept of these, I am no good with slope and tables. ;-;

zubka84 [21]

Answer:

1. -4

2. 6

3. -6

(i hope this is right •_•)

Step-by-step explanation:

First table

When the x coordinate is 0, that point is your y intercept. For the first one, your y intercept is -4.

Second table

For the second one, we need to do a bit of counting. We can see the x coordinates go before and after zero, but the table does not show us 0. So, we're going to have to calculate the slope. Bear with me here, I'm a little tired and this might be rambling ;-;

So, the formula for calculating slope is $\frac{y_{2} -y_{1}}{x_{2}-x_{1}}$ . I'm going to use those first two points to get my slope. We're going to say the first point is point 1 and the second point is point 2 (genius, i know lol). So, let's substitute in the x and y values.

$\frac{9-12}{-3-(-6)}$

And simplify...

$\frac{-3}{3}$

So, your slope is -1. We can use that. We just have to count down.

If the x is -2, the y is 8. If the x is -1, the y is 7. And if the x is 0....(drumroll please) the y is 6! So, your y intercept is 6.

Third table

Now, this table isn't very nice either and doesn't have an x as 0 for us. Hmpf. But we can still do what we did above. I'll just skip the explanation and you can observe my steps.

$\frac{-3-(-5)}{9-3}$