If the graph of the following parabola is shifted two units left and three units down, what is the resulting equation?
1 answer:
Answer:
Step-by-step explanation:
Because the x and y have been reversed in this equation, shifting the parabola to the left will be outside of the exponent and shifting up and down will be inside with the exponent.
The equation becomes .
Where subtracting by 2 moves it two units to the left and adding by 3 moves it 3 units down.
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Answer:
Step-by-step explanation:
If you plot this point and the directrix on a coordinate plane, you can see that the directrix is 1/4 of a unit below the vertex. Since, by nature, a parabola opens in the direction opposite the directrix and "hugs" the focus, this is a positive x-squared parabola (meaning it opens upwards). The formula for this type of a parabola is, in vertex form,
where p is distance (in units) between the vertex and the directrix and h and k are the coordinates of the vertex. For us, p = .25, h = 7, and k = -6. Filling in our formula:
Simplify the left side to
which simplifies, in its entirety, to