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Express the function f(x) = 4x^2 - 12x + 5 in factored form and f(x) = -5x^2 + 20x + 2...

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sodapopjo | Student, Grade 11 | Honors

Posted August 24, 2012 at 2:16 PM via web

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Express the function f(x) = 4x^2 - 12x + 5 in factored form and f(x) = -5x^2 + 20x + 2 in vertex form.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted August 24, 2012 at 2:23 PM (Answer #1)

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The function f(x) = 4x^2 - 12x + 5 has to be expressed in the factored form.

4x^2 - 12x + 5

=> 4x^2 - 10x - 2x + 5

=> 2x(2x - 5) - 1(2x - 5)

=> (2x - 1)(2x - 5)

f(x) = -5x^2 + 20x + 2 has to be expressed in vertex form

-5x^2 + 20x + 2

=> -5(x^2 - 4x) + 2

=> -5(x^2 - 4x + 4) + 2 + 20

=> -5(x - 2)^2 + 22

The given functions `f(x) = 4x^2 - 12x + 5 => f(x) = (2x - 1)(2x - 5)` and `f(x) = -5x^2 + 20x + 2 => f(x) = -5(x - 2)^2 + 22`

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