Pregunta
Toplic realize. Topiew (LMS graded)
Part 1 of 2
Find the zeros of the function, and then describe the behavior of the graph at each zero.
Part 1 of 2
Find the zeros of the function, and then describe the behavior of the graph at each zero.
Ask by Ingram Owen. in the United States
Dec 27,2024
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The zeros of the function
are
and
. At
, the graph crosses the x-axis, and at
, it touches the x-axis and turns around without crossing.
Solución

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Como
Bonus Knowledge
To find the zeros of the function
, we can start by factoring out the greatest common factor, which is
:
Next, we can further factor the quadratic part:
Thus, our factored function is:
Setting the function to zero to find the zeros, we have:
From here, we can see that the zeros are:
-
-
(with multiplicity 2)
Now, let’s discuss the behavior of the graph at these zeros:
- At
, the graph crosses the x-axis since it’s a simple zero (multiplicity of 1). - At
, because of the multiplicity of 2, the graph touches the x-axis and bounces back up, rather than crossing over.
So, we have one crossing point at
and a bouncing point at
. Happy graphing!

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