Question

Calculate the range of values of c for which 3x2-9x + c> 2.25 for all values of X​

Answer 1

Answer:y = 3 x^2 - 9 x + c is an upward opening parabola so we want the vertex at y = 2.25

3 x^2 - 9 x = y-c

x^2 - 3 x = y/3 - c/3

x^2 - 3 x + 9/4 = y/3 -c/3 + 9/4

(x-3/2)^2 = (1/3)(y -c +27/4)

c-27/4 = 2.25 = 9/4

c = 36/4 = 9

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Now check

if c = 9

3 x^2 - 9 x + 9 = y

x^2 - 3 x = y/3-3

x^2 -3 x + 9/4 = y/3 -12/4 + 9/4

(x-3/2)^2 = y/3 - 3/4 = (1/3 ) (y- 9/4)

9/4 = 2.25 sure enough

Step-by-step explanation:

Answer 2

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Given:

Find the range values of c for which 3x^2 - 9x + c > 2.25 for all values of c.

To Find :

Anonymous

Mar 18, 2018

y = 3 x^2 - 9 x + c is an upward opening parabola so we want the vertex at y = 2.25

Rate of explanation :

3 x^2 - 9 x = y-c

x^2 - 3 x = y/3 - c/3

x^2 - 3 x + 9/4 = y/3 -c/3 + 9/4

(x-3/2)^2 = (1/3)(y -c +27/4)

c-27/4 = 2.25 = 9/4

c = 36/4 = 9

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Step by step solution :

Now check

if c = 9

3 x^2 - 9 x + 9 = y

x^2 - 3 x = y/3-3

x^2 -3 x + 9/4 = y/3 -12/4 + 9/4

(x-3/2)^2 = y/3 - 3/4 = (1/3 ) (y- 9/4)

9/4 = 2.25 sure enough

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Hope my answer will be helpful for you thanks . . .