Pregunta
Write the quadratic function \( f(x)=-6(x-1)^{2}+24 \)
Ask by Garrett Li. in the United States
Dec 03,2024
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The quadratic function is \( f(x)=-6(x-1)^{2}+24 \).
Solución
The quadratic function is given by \( f(x)=-6(x-1)^{2}+24 \).
This function is in vertex form, where the vertex is at the point \((h, k)\) and the equation is given by \( f(x)=a(x-h)^{2}+k \).
Comparing the given function with the vertex form, we can see that:
- \( a = -6 \)
- \( h = 1 \)
- \( k = 24 \)
Therefore, the quadratic function is \( f(x)=-6(x-1)^{2}+24 \).
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Simplifique esta solución Beyond the Answer
To write the quadratic function in standard form, we'll expand \( f(x) = -6(x-1)^{2} + 24 \). First, we expand the squared term: \[ (x-1)^{2} = x^2 - 2x + 1 \] Now, substituting back into the function: \[ f(x) = -6(x^2 - 2x + 1) + 24 \] Distributing the -6: \[ f(x) = -6x^2 + 12x - 6 + 24 \] Combining like terms gives: \[ f(x) = -6x^2 + 12x + 18 \] So the standard form of the quadratic function is: \[ f(x) = -6x^2 + 12x + 18. \]
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