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
Step-by-step 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
- 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
