Question
Which function has a vertex at (3, -9) and zeros at x = 0 and x = 6?
f(x)=x^2-3x −9
f(x)=x^2+3x −9
f(x)=x^2-6x
f(x)=x^2+6x
f(x)=x^2-3x −9
f(x)=x^2+3x −9
f(x)=x^2-6x
f(x)=x^2+6x
Answers
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Answered by
GPT 3.5
To find the function that has a vertex at (3, -9) and zeros at x = 0 and x = 6, we can start by finding the equation of a parabola in vertex form.
The vertex form of a parabola is given by:
f(x) = a(x - h)^2 + k
Where (h, k) is the vertex of the parabola.
Given that the vertex is at (3, -9), we have h = 3 and k = -9.
Next, we can rewrite the equation with the zeros:
f(x) = a(x - 0)(x - 6)
Solving for a, we substitute the vertex coordinates:
-9 = a(3 - 0)^2
-9 = 9a
a = -1
So, the function will be:
f(x) = -(x)(x - 6)
f(x) = -x^2 + 6x
Therefore, the function is f(x) = -x^2 + 6x.
The vertex form of a parabola is given by:
f(x) = a(x - h)^2 + k
Where (h, k) is the vertex of the parabola.
Given that the vertex is at (3, -9), we have h = 3 and k = -9.
Next, we can rewrite the equation with the zeros:
f(x) = a(x - 0)(x - 6)
Solving for a, we substitute the vertex coordinates:
-9 = a(3 - 0)^2
-9 = 9a
a = -1
So, the function will be:
f(x) = -(x)(x - 6)
f(x) = -x^2 + 6x
Therefore, the function is f(x) = -x^2 + 6x.
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