Respuesta :

kudzordzifrancis

Answer:

B. (4,9), maximum

Step-by-step explanation:

The given function is

[tex]y=-1(x-4)^2+9[/tex]

This function is of the form;

[tex]y=a(x-h)^2+k[/tex]

where (h,k)=(4,9) is the vertex.

and [tex]a=-1[/tex] since 'a' is negative the vertex is the maximum point on the graph of this function.

The correct answer is B

luisejr77

Answer: option B

Step-by-step explanation:

Given the quadratic equation [tex]y=-1(x-4)^2+9[/tex], you can use the formula to find the x-coordinate of the vertex of the parabola:

[tex]x=\frac{-b}{2a}[/tex]

Simplify the quadratic equation. Remember that:

[tex](a-b)^2=a^2-2ab+b^2[/tex]

Then:

[tex]y=-1(x-4)^2+9\\y=-1(x^2-2(x)(4)+4^2)+9\\y=-x^2+8x-16+9\\y=-x^2+8x-7[/tex]

Substituting:

[tex]x=\frac{-8}{2(-1)}=4[/tex]

The y-coordinate is:

[tex]y=-(4)^2+8(4)-7=9[/tex]

The vertex is at (4,9) therefore it is a maximum.

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