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.