Which is the equation of the parabola with a leading coefficient of
minus, one third−
3
1
and a vertex left parenthesis, minus, 1, comma, 9, right parenthesis(−1,9) ?
Answer
Attempt 1 out of 2
Multiple Choice Answers
f, of, x, equals, minus, one third, left parenthesis, x, minus, 1, right parenthesis, squared, plus, 9f(x)=−
3
1
(x−1)
2
+9
f, of, x, equals, minus, one third, left parenthesis, x, plus, 1, right parenthesis, squared, plus, 9f(x)=−
3
1
(x+1)
2
+9
f, of, x, equals, minus, one third, left parenthesis, x, minus, 1, right parenthesis, squared, minus, 9f(x)=−
3
1
(x−1)
2
−9
f, of, x, equals, minus, one third, left parenthesis, x, plus, 1, right parenthesis, squared, minus, 9f(x)=−
3
1
(x+1)
2
−9
1 answer
To find the equation of the parabola with a given vertex and leading coefficient, we can use the vertex form of a parabola:
\[
f(x) = a(x - h)^2 + k
\]
where \((h, k)\) is the vertex and \(a\) is the leading coefficient.
Given:
- Leading coefficient \(a = -\frac{1}{3}\)
- Vertex \( (h, k) = (-1, 9) \)
Substituting these values into the vertex form:
\[
f(x) = -\frac{1}{3}(x - (-1))^2 + 9
\]
This simplifies to:
\[
f(x) = -\frac{1}{3}(x + 1)^2 + 9
\]
Now, we need to match this with the multiple choice answers provided.
The correct choice is:
\[
f(x) = -\frac{1}{3}(x + 1)^2 + 9
\]
So the correct answer is:
f(x) = −\frac{1}{3}(x + 1)^2 + 9.
1 answer