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Contact [7]
3 years ago
10

Write f(x)=8x^2-4x+11 in vertex form

Mathematics
1 answer:
Vlad [161]3 years ago
3 0

Answer:

f(x)=8(x-\frac{1}{4})^{2}+\frac{21}{2}

or

f(x)=8(x-0.25)^{2}+10.5

Step-by-step explanation:

we have

f(x)=8x^{2}-4x+11

This is a vertical parabola open upward (because the leading coefficient is positive)

The vertex is a minimum

Convert to vertex form

Factor the leading coefficient

f(x)=8(x^{2}-\frac{1}{2}x)+11

Complete the square. Remember to balance the equation by adding the same constants to each side.

f(x)=8(x^{2}-\frac{1}{2}x+\frac{1}{16})+11-\frac{1}{2}

f(x)=8(x^{2}-\frac{1}{2}x+\frac{1}{16})+\frac{21}{2}

Rewrite as perfect squares

f(x)=8(x-\frac{1}{4})^{2}+\frac{21}{2} ----> equation in vertex form

or

f(x)=8(x-0.25)^{2}+10.5

The vertex is the point  (0.25,10.5)

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The sum of a minutes and b seconds, expressed in minutes, is:​
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(1+b/60) minutes

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For the Community Gym:
Membership Charge = $50
Monthly fee = $55
So for the 1st month total charge = $(50 +55)
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For each month the member pays $55
So after the 2nd month total payment = $(105 + 55)
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After 3rd month total payment = $(160 + 55)
                                                 = $215
After 4th month total payment = $(215 + 55)
                                                 = $270
After 5th month total payment = $(270 + 55)
                                                 = $325
After 6th month total payment = $(325 + 55)
                                                 = $380
Now for the Workout Gym:
Membership Charge = $200
Monthly Charge = $45
So for the 1st month the member pays = $(200 + 45)
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For the 2nd month total payment = $( 245 +45)
                                                      = $290
For the 3rd month total payment = $(290 + 45)
                                                     = $335
For the 4th month total payment = $(335 + 45)
                                                     = $ 380
So the 6th month payment in the Community Gym is the same as the 4th month payment in the Workout Gym. The amount will be $380.
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