Pregunta
Given the following function, (a) find the vertex, (b) determine whether there is a maximum or a minimum value, and find the value; © find the range; and (d) find the intervals on which the function
is increasing and the intervals on which the function is decreasing
(a) The vertex is
(Type an ordered pair, usiipg integers or fractions.)
is increasing and the intervals on which the function is decreasing
(a) The vertex is
(Type an ordered pair, usiipg integers or fractions.)
Ask by Medina Hart. in the United States
Nov 07,2024
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
(a) The vertex is
.
(b) The function has a maximum value of
.
© The range is
.
(d) The function is increasing on
and decreasing on
.
Solución

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Como
Beyond the Answer
To find the vertex of the function
, we can use the vertex formula
. Here,
and
.
Calculating the x-coordinate of the vertex:
Now, substituting
back into the function to find the y-coordinate:
So, the vertex is
.
To answer part (b), since the coefficient of
is negative, the parabola opens downwards, indicating that there is a maximum value at the vertex. The maximum value is
.
For part ©, since the parabola opens downwards, the range of the function is:
For part (d), to determine the intervals on which the function is increasing and decreasing, we can analyze the derivative or the vertex. The function increases on the interval
and decreases on
.
So the answers are:
(a) The vertex is .
(a) The vertex is

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