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I don’t understand this question

I don’t understand this question-example-1
User Diegog
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1 Answer

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20 votes

Answer:

f(-4) = - 64

f(3) = - 15

f(-a) = - 3a² - 4a

-f(a) = 3a² - 4a

f(a + h) = - 3a² - 6ah - 3h² + 4a + 4h

Pay careful attention that you do not miss the negative signs in some of these terms

Explanation:

The function is f(x) = -3x² + 4x

To evaluate the function at any value of x, simply substitute for x in the function expression

  1. f(-4)
    = -3(-4)² + 4(-4) = -3 x 16 - 16 = -48-16 = - 64 since (-4)² = 16
    So f(-4) = - 64

  • f(3) = -3(3)² + 4(3) = -3 x 9 + 12 = -27 + 12 = - 15
    So f(3) = - 15
  • f(-a) = -3(-a)² + 4(-a) = - 3a² - 4a
    So f(-a) = - 3a² - 4a
  • -f(a)
    To find -f(a) , first compute f(a) = -3(a)² + 4(a) = - 3a² + 4a, then add a negative sign in front and expand the brackets:
    -f(a) = - (- 3a² + 4a) = + 3a² - 4a = 3a² - 4a
    So -f(a) = 3a² - 4a

  • f(a + h)
    = - 3(a + h)² + 4(a + h)

    (a + h)² = a² + 2ah + h²
    done by applying perfect squares formula where (a + b)² = a² + 2ab + b² except instead of b we are using h

    f(a + h) = - 3(a + h)² + 4(a + h)
    = - 3(a² + 2ah + h² ) + 4(a + h)

    Expanding the brackets,
    = - 3a² - 3(2ah) - 3h² + 4a + 4h
    = - 3a² - 6ah - 3h² + 4a + 4h
    So f(a + h ) = - 3a² - 6ah - 3h² + 4a + 4h


User Evan Salter
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