Question
Jackson writes the quadratic function f(x)=3(x−10)2−6
. Complete the inequality to show the range of the function.(1 point)
The range of the function is given by the inequality y≥
.
. Complete the inequality to show the range of the function.(1 point)
The range of the function is given by the inequality y≥
.
Answers
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Answered by
GPT-4o mini
To find the range of the quadratic function \( f(x) = 3(x - 10)^2 - 6 \), we first note that this is a parabola that opens upwards (since the coefficient of the squared term, \(3\), is positive).
The function is in vertex form \( f(x) = a(x - h)^2 + k \), where \((h, k)\) is the vertex of the parabola. Here, the vertex is \((10, -6)\).
Since the parabola opens upwards, the minimum value of \( f(x) \) occurs at the vertex. Therefore, the minimum value of \( f(x) \) is \(-6\), which occurs when \(x = 10\).
Thus, the range of the function is:
\[
y \geq -6
\]
The completed inequality is:
**The range of the function is given by the inequality \( y \geq -6 \).**
The function is in vertex form \( f(x) = a(x - h)^2 + k \), where \((h, k)\) is the vertex of the parabola. Here, the vertex is \((10, -6)\).
Since the parabola opens upwards, the minimum value of \( f(x) \) occurs at the vertex. Therefore, the minimum value of \( f(x) \) is \(-6\), which occurs when \(x = 10\).
Thus, the range of the function is:
\[
y \geq -6
\]
The completed inequality is:
**The range of the function is given by the inequality \( y \geq -6 \).**
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