What is the vertex of # y=x^2/7-7x+1 #?

Answer 1

#(24.5,-84.75)#

#y= =>a=1/7,b=-7,c=1# for co-ordinate of vertex #(h,k)# #h=-b/(2a)=7/(2.(1/7))=49/2# put #x=49/2# to find #y# and corresponding point #k# #k=-84.75# co-ordinate is #(24.5,-84.75)#
best method : by calculus vertex is the lowermost(or uppermost) point #i.e# minimum or maximum of the function we have #y=x^2/7-7x+1# #=>(dy)/(dx)=2x/7-7# at minimum or maximum slope of curve is 0 or #(dy)/(dx)=0# #=>2x/7-7=0=>x=49/2#

check if this point is of maximum or minimum by second derivative test(thisstep is not necessarily needed) if second derivative is -ve it corresponds to point of maximum if second derivative is +ve it corresponds to point of minimum

#(d^2y)/(dx^2)=2/7=+ve=>x=49/2# corresponds to point of minimum now put #x=49/2# to find #y# and you will find coordinates as #(24.5,-84.75)# and it's evident from the graph

graph{x^2/7-7x+1 [-10, 10, -5, 5]}

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Answer 2

The vertex of the function ( y = \frac{x^2}{7} - 7x + 1 ) can be found using the formula for the x-coordinate of the vertex, which is given by ( x = -\frac{b}{2a} ) in the standard form of a quadratic function ( y = ax^2 + bx + c ). In this case, ( a = \frac{1}{7} ) and ( b = -7 ). Plugging these values into the formula, we get:

( x = -\frac{(-7)}{2 \cdot \frac{1}{7}} )

Simplifying further:

( x = -\frac{-7}{\frac{2}{7}} )

( x = -\frac{-49}{2} )

( x = \frac{49}{2} )

Now, substitute this value of ( x ) into the original function to find the corresponding y-coordinate:

( y = \frac{(\frac{49}{2})^2}{7} - 7(\frac{49}{2}) + 1 )

( y = \frac{2401}{28} - \frac{343}{2} + 1 )

( y = 85.75 )

So, the vertex of the function is ( \left(\frac{49}{2}, 85.75\right) ).

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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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