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Select the correct answer.
The number of customers in a store during the midday hours of 10 a.m. to 5 p.m. can be modeled by this function, where n is the number of
customers thours after 10 a.m.
n = 2t2 - 8t + 15
Rewrite the equation to reveal the minimum number of customers. At what time does that minimum occur?
OA n = 2(t - 2)2 + 15; 2 p.m.
OB n = 2(t - 4)2 + 7;3 p.m.
OC n = 2(t - 2)2 + 7; 12 p.m.
OD. n= 2(t – 4)2 + 1; 4 p.m.

Select the correct answer The number of customers in a store during the midday hours of 10 am to 5 pm can be modeled by this function where n is the number of c class=

Respuesta :

Using the vertex of the equation, it is found that the correct option regarding the minimum number is given by:

C. n = 2(t - 2)² + 7.

What is the equation of a parabola given it’s vertex?

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

Considering a standard equation, given by:

y = ax² + bx + c.

The vertex is given by:

[tex](h,k) = \left(-\frac{b}{2a}, -\frac{b^2 - 4ac}{4a}\right)[/tex].

If a is positive, the vertex is a minimum value.

In this problem, the equation is given by:

n = 2t² - 8t + 15.

The coefficients are: a = 2, b = -8, c = 15.

Hence:

[tex]h = -\frac{b}{2a} = \frac{8}{4} = 2[/tex].

[tex]k = -\frac{(-8)^2 - 4(2)(15)}{4(2)}\right) = 7[/tex]

The minimum is 2 hours after 10 a.m., hence 12 p.m, and the function is:

C. n = 2(t - 2)² + 7.

More can be learned about the vertex of a quadratic equation at https://brainly.com/question/24737967

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