Pregunta
What are the \( x \)-intercepts of the following function? \( f(x)=(x-2)(x+5)(x-7) \) \( 2,5,7 \) \( -2,5,-7 \) \( 2,-5,7 \) 5,7
Ask by Wade Mckenzie. in the United States
Jan 30,2025
Solución de tutoría real
Respuesta verificada por el tutor
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The \( x \)-intercepts are at \( x = 2 \), \( x = -5 \), and \( x = 7 \).
Solución
To find the \( x \)-intercepts of the function \( f(x) = (x - 2)(x + 5)(x - 7) \), we need to determine the values of \( x \) that make \( f(x) = 0 \).
Set each factor equal to zero and solve for \( x \):
1. \( x - 2 = 0 \)
\( \Rightarrow x = 2 \)
2. \( x + 5 = 0 \)
\( \Rightarrow x = -5 \)
3. \( x - 7 = 0 \)
\( \Rightarrow x = 7 \)
Therefore, the \( x \)-intercepts are at \( x = 2 \), \( x = -5 \), and \( x = 7 \).
**Correct Answer:** \( 2,-5,7 \)
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución Mind Expander
To find the \( x \)-intercepts of the function \( f(x)=(x-2)(x+5)(x-7) \), you simply set the function equal to zero: \( f(x) = 0 \). This leads to three equations: \( x - 2 = 0 \), \( x + 5 = 0 \), and \( x - 7 = 0 \). Solving these gives the intercepts \( x = 2 \), \( x = -5 \), and \( x = 7 \). So, the \( x \)-intercepts are \( 2, -5, 7 \). A handy way to remember finding \( x \)-intercepts is to keep in mind this simple method: **set the factored equation to zero!** Each factor gives you a direct path to the intercepts. Just be cautious about negative signs!
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