Answer:
y = -1/10x^2 +2.5
Step-by-step explanation:
The distance from focus to directrix is twice the distance from focus to vertex. The focus-directrix distance is the difference in y-values:
-1 -4 = -5
So, the distance from focus to vertex is p = -5/2 = -2.5. This places the focus 2.5 units below the vertex. Then the vertex is at (h, k) = (0, -1) +(0, 2.5) = (0, 1.5).
The scale factor of the parabola is 1/(4p) = 1/(4(-2.5)) = -1/10. Then the equation of the parabola is ...
y = (1/(4p))(x -h) +k
y = -1/10x^2 +2.5
_____
You can check the graph by making sure the focus and directrix are the same distance from the parabola everywhere. Of course, if the vertex is halfway between focus and directrix, the distances are the same there. Another point that is usually easy to check is the point on the parabola that is even with the focus. It should be as far from the focus as it is from the directrix. In this parabola, the focus is 5 units from the directrix, and we see the points on the parabola at y=-1 are 5 units from the focus.
Answer:
Ammm, I think the answer you have is wrong, but what I really think is that the equations you put in are not the right ones because the answer for these is "ugly" (decimals etc...). Want to check your equations?
Step-by-step explanation:
Here is a step by step explanation to your equations (I assumed +3z for the second but you can change it). You can edit it for your equations if you want to.
https://simplisico.com/share/q/QiWKOyN5uYgkSG4iBXOmdG0i
<span>Consider the equation 3p - 7 + p = 13. What is the resulting equation after the first step in the solution?</span>
Opposite sides are congruent opposite angles are congruent
Answer:
1.7689 (rounded to 4 decimal places)
Step-by-step explanation:
Let the number we are seeking be "x", thus we can write the equation as:

Since we have raised "x" to the "10th power", to get "x" back again, we need to take 10th root. Same goes for right side, we take 10th root of 300. We will get our answer. The process shown below:
![x^{10}=300\\\sqrt[10]{x^{10}} =\sqrt[10]{300} \\x=\sqrt[10]{300} \\x=1.7689](https://tex.z-dn.net/?f=x%5E%7B10%7D%3D300%5C%5C%5Csqrt%5B10%5D%7Bx%5E%7B10%7D%7D%20%3D%5Csqrt%5B10%5D%7B300%7D%20%5C%5Cx%3D%5Csqrt%5B10%5D%7B300%7D%20%5C%5Cx%3D1.7689)
hence, 1.7689 raised to 10th power will give us 300