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DaniilM [7]
3 years ago
9

What are the coordinates of the vertex for the function shown below ?

Mathematics
1 answer:
Anuta_ua [19.1K]3 years ago
6 0

Answer:

Step-by-step explanation:

We can answer this in two ways:  Differentiation and Graphing.

<u>Differentitate:</u>

The first derivative of a function yields a function that provides the slope for any point on the line of the original function.  The slope of a vertex is zero, so we can set the first derivative to 0 and solve for x.

f(x) = 3(x-1)^2 + 4

f(x) = 3(x-1)(x-1) + 4

f(x) = 3(x^2 - 2x + 1) + 4

f(x) = 3x^2 - 6x + 7

f'(x) = 6x -6

Set this = 0 and find x:

0 = 6x -6

x = 1

The value of y when x=1 in the original equation is:

f(1) = 3(1-1)^2 + 4

y = 4

The vertex is (1,4)

<u>Graph:</u>

You can use DESMOS to plot the function.  The result is attached.  Look for the vertex and read the coordinates.  (1,4) seems to work.

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sveta [45]

\text{Hey there!}

\mathsf{-\dfrac{5}{2}a+5=25}

\text{\bf{SUBTRACT}}\mathsf{\ by\ 5\ on\ your\ sides}\\\mathsf{-\dfrac{5}{2}a+5-5=25-5}\\\\\mathsf{Cancel\ out: 5-5\ because\ it\ gives\ you\ 0}\\\\\mathsf{Keep: 25 - 5\ because\ it\ helps\ us\ solve\ for\ a}\\\\\mathsf{25-5=20}\\\\\mathsf{New\ equation:- \dfrac{5}{2}a=20}

\text{\bf{MULTIPLY}}\mathsf{\  \dfrac{2}{-5}\ on\ your\ sides}\\\\\mathsf{\dfrac{2}{=5}\times\dfrac{-5}{2}a=\dfrac{2}{-5}\times20}\\\\\mathsf{Cancel\ out: \dfrac{2}{-5}\times\dfrac{-5}{2}\ because\ it\ gives\ you\ 1}\\\\\mathsf{Keep: \dfrac{2}{-5}\times20\ because\ it\ gives\ you\ the\ value\ of\ a}\\\\\mathsf{\dfrac{2}{-5}\times20=-8}

\boxed{\boxed{\boxed{\boxed{\mathsf{Thus\ your\ answer\boxed{\boxed{\mathsf{a=-8}}}}}}}}\checkmark

\large\text{Good luck on your assignment and enjoy your day!}

~\dfrac{\frak{LoveYourselfFirst}}{:)}

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