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photoshop1234 [79]
3 years ago
5

y = x2 - 6x - 8 Complete the square in the quadratic equation in order to write the equation in vertex form.

Mathematics
1 answer:
Airida [17]3 years ago
8 0

Answer:

y = (x-3)^2 - 17

Step-by-step explanation:

To complete the square, take the middle term bx and divide it in two. Then take the square.

x^2 - 6x - 8 has bx = -6x. Take -6/2 = -3. Square -3^2 = 9.

Now to finish completing the square add 9 and subtract 9 from one side.

y = x^2 - 6x - 8

y = (x^2 - 6x +9) -9 - 8

y = (x-3)^2 - 17

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ANSWER

See below

EXPLANATION

Part a)

The given function is

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b) Using calculus, we find the first derivative of the given function.

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This implies that,

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We plug this values into the original function to obtain the y-values of the turning points

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f''( -  \frac{ \sqrt{15} }{5} ) \:   <  \: 0

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(   -  \frac{ \sqrt{15} }{5}  , \frac{1}{125} ( 6 \sqrt{15}  + 750))

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f''( \frac{ \sqrt{15} }{5} ) \:    >  \: 0

Hence

(     \frac{ \sqrt{15} }{5}  , \frac{1}{125} (- 6 \sqrt{15}  + 750))

is a minimum point.

f''(0) \: =\: 0

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