NEED HELP ASAP: Let f(x)=x2−6x+13 . What is the vertex form of f(x)? What is the minimum value of f(x)? Enter your answers in the boxes. Vertex form: f(x)= Minimum value of f(x):

The vertex form of [tex]f(x)=ax^2+bx+c[/tex]
[tex]f(x)=a(x-h)^2+k[/tex]

where: [tex]h=\dfrac{-b}{2a};\ k=f(h)[/tex]

We have: [tex]f(x)=x^2-6x+13\to a=1;\ b=-6;\ c=13[/tex]

substitute:
[tex]h=\dfrac{-(-6)}{2\cdot1}=\dfrac{6}{2}=3\\\\k=f(3)=3^2-6\cdot3+13=9-18+13=4[/tex]
The vertex form of f(x):
[tex]f(x)=(x-3)^2+4[/tex]
The value of minimum is equal k.
Therefore: [tex]y_{min}=4[/tex]

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ap8997154 ap8997154 · Answer 2 · 2022-05-21T12:22:50+02:00

A quadratic equation is written in the form of ax²+bx+c. The vertex form of the quadratic equation, f(x)=x²−6x+13, will be f(x)=(x-3)²+4.

What is a quadratic equation?

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.

The vertex form of a quadratic equation is written as a(x-h)²+k. The value of (h,k) is found using the formula.

h = -b/2a

k = f(h)

Now in the given equation, f(x)=x²−6x+13, the value of a, b and c, will be written as 1, -6, and 13, respectively. Therefore, the value of h will be,

h = -b/2a = -(-6)/2(1) = 3

k = f(3) = 3²-6(3)+13 = 4

Hence, the vertex form of the quadratic equation, f(x)=x²−6x+13, will be f(x)=(x-3)²+4.

Learn more about Quadratic Equations:

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NEED HELP ASAP: Let ​ f(x)=x2−6x+13 ​ . What is the vertex form of f(x)? What is the minimum value of f(x)? Enter your answers in the boxes. Vertex form: f(x)= Minimum value of f(x):

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What is a quadratic equation?

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NEED HELP ASAP: Let f(x)=x2−6x+13 . What is the vertex form of f(x)? What is the minimum value of f(x)? Enter your answers in the boxes. Vertex form: f(x)= Minimum value of f(x):