How do you find the vertex of #y= x^2-8x+5#?

Answer 1

The simplest method for finding the vertex of the given polynomial is to convert it into "vertex form" to find the vertex at #(4,-11)#

Considering #y=x^2-8x+5#
The vertex will be at #(a,b)# if we can translate this into vertex form: #color(white)("XXXX")##y=m(x-a)^2+b# #color(white)("XXXX")##color(white)("XXXX")#for some constants #a# and #b#.

The "completion of the square method" is the simplest way to accomplish this conversion.

#color(white)("XXXX")#color(white)("XXXX")#note: #(m+n)^2 = (m^2+2mn+n^2)# if the first two terms of a squared binomial are #x^2-8x#, then the third term must be #((-8x)/(2x))^2 = 16#.
To "complete the square," we add #16# and then subtract it.
(x^2-8x+16) + 5 -16# = #y
The simplified form is #y = (x-4)^2 + (-11)#, and the desired "vertex form" (with #m=1#) is #color(white)("XXXX")#.
Vertex is therefore at #(4,-11)#.
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Answer 2

Find vertex of f(x) = x^2 - 8x + 5

Ans: Vertex (4, -11)

Vertex's x-coordinate is #x = -b/(2a) = 8/2 = 4#.
The vertex's y-coordinate is #y = f(4) = 4^2 - 8(4) + 5 = - 11#
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Answer 3

To find the vertex of the quadratic function ( y = x^2 - 8x + 5 ), you can use the formula ( x = -\frac{b}{2a} ). In this equation, ( a ) represents the coefficient of the ( x^2 ) term, and ( b ) represents the coefficient of the ( x ) term. Plugging the values ( a = 1 ) and ( b = -8 ) into the formula, you get ( x = -\frac{-8}{2(1)} ), which simplifies to ( x = 4 ). To find the corresponding ( y )-coordinate, substitute ( x = 4 ) into the original function: ( y = (4)^2 - 8(4) + 5 = 16 - 32 + 5 = -11 ). Therefore, the vertex of the function is ( (4, -11) ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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