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Part of a logo on a business card is modeled by the function f(x)=-(x-1)^2+1.5. The function gives the vertical height as a function of the horizontal distance in inches. What is the greatest vertical distance of the design?
1. 0.5 in
2. 1.0 in
3. 1.5 in
4. 2.5 in

Respuesta :

msm555

Answer:

3: [tex] 1.5 [/tex] in

Step-by-step explanation:

To find the greatest vertical distance of the design, we need to analyze the function [tex] f(x) = -(x - 1)^2 + 1.5 [/tex].

This function is in vertex form:

[tex] \Large\boxed{\boxed{f(x) = a(x - h)^2 + k }}[/tex]

where

  • [tex](h, k)[/tex] is the vertex of the parabola.

Comparing the given function to the vertex form, we can see that [tex] h = 1 [/tex] and [tex] k = 1.5 [/tex].

The vertex of the parabola is at the point [tex](1, 1.5)[/tex].

The maximum or minimum of the quadratic function occurs at the vertex. Since the coefficient of [tex] (x - 1)^2 [/tex] is negative, the parabola opens downward, and the vertex represents the maximum point.

Therefore, the greatest vertical distance of the design is the [tex] y [/tex]-coordinate of the vertex, which is [tex] 1.5 [/tex] inches.

So, the correct answer is:
3: [tex] 1.5 [/tex] in

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