SOLUTION: The vertex of this parabola is at (-3, -1). When the y-value is 0, the x-value is 4. What is the coefficient of the squared term in the parabola's equation?

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: The vertex of this parabola is at (-3, -1). When the y-value is 0, the x-value is 4. What is the coefficient of the squared term in the parabola's equation?       Log On


   

Question 966396: The vertex of this parabola is at (-3, -1). When the y-value is 0, the x-value is 4. What is the coefficient of the squared term in the parabola's equation?

Found 2 solutions by Fombitz, MathLover1:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the vertex form,
y=a%28x-h%29%5E2%2Bk
y=a%28x%2B3%29%5E2-1
Use the point to solve for a,
0=a%284%2B3%29%5E2-1
1=a%287%5E2%29
a=1%2F49
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Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
the vertex of this parabola is at (-3, -1)
when the y-value is 0, the x-value is 4
so, you are given two points that lie on a parabola and we can use them to find equation
since one point is a vertex, use vertex form:
y=a%28x-h%29%5E2%2Bk where h=-3 and k=-1
y=a%28x-%28-3%29%29%5E2-1
y=a%28x%2B3%29%5E2-1
y=a%28x%5E2%2B6x%2B9%29-1
y=ax%5E2%2B6ax%2B9a-1
use the y-value is 0, the x-value is 4
0=a%2A4%5E2%2B6%2A4%2B9%2A4-1
0+=+49a-1
1=49a
1%2F49=a the coefficient of the squared term in the parabola's equation
and your equation is:
y=%281%2F49%29%28x%2B3%29%5E2-1