SOLUTION: I do not understand how to do this. Please help me. The vertex of this parabola is at (1, -4). When the y-value is -5, the x-value is 4. What is the coefficient of the squared t

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: I do not understand how to do this. Please help me. The vertex of this parabola is at (1, -4). When the y-value is -5, the x-value is 4. What is the coefficient of the squared t      Log On


   

Question 1201025: I do not understand how to do this. Please help me.
The vertex of this parabola is at (1, -4). When the y-value is -5, the x-value is 4. What is the coefficient of the squared term in the equation of this parabola?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


I will assume the parabola opens upward or downward -- i.e., the equation of the parabola in vertex form is y%2B4=a%28x-1%29%5E2. Then, using the other given point (4,-5)...

-5%2B4=a%284-1%29%5E2
-1=9a
a=-1%2F9

ANSWER: -1/9

Once you get familiar with equations of parabolas, you can get that answer without doing the formal algebra.

The given point is 3 units to the right of the vertex; if the leading coefficient were 1 then the y coordinate of the second point would be 3^2=9 more than the y coordinate of the vertex.

But the y coordinate of the second point is 1 less than the y coordinate of the vertex, so the leading coefficient is -1/9.