For the following find f(5),f(-3),f(x+1),f(x-2)?

Question

f(x)=2x^2-3x+6

if you could show the work and explain the steps so i can do the rest of my homework that would be great! thanks in advance!

Answer 1

f(x) = 2x² - 3x + 6 ---------------> (1)

Substitute x = 5 in the equation (1).

f(5) = 2(5)² - 3(5) + 6 = 2(25) - 15 + 6 = 50 - 9 = 41.

Substitute x = -3 in the equation (1).

f(5) = 2(-3)² - 3(-3) + 6 = 2(9) + 9 + 6 = 18 + 15 = 33.

Substitute x = (x + 1) in the equation (1).

f(x + 1) = 2(x+1)² - 3(x + 1) + 6.

Principal algebraic expressions and formula: (a + b)² = a² + 2ab + b²

Distribute terms using distributive property:  a( b + c) = ab + ac

f(x + 1) = 2(x²+2x+1) - 3x - 3 + 6 = 2x² + 4x + 2 - 3x + 3 = 2x² + x + 5

Substitute x = (x - 2) in the equation (1).

f(x - 2) = 2(x - 2)² - 3(x - 2) + 6.

Principal algebraic expressions and formula: (a + b)² = a² + 2ab + b².

Distribute terms using distributive property:  a( b + c) = ab + ac.

f(x - 2) = 2(x²-4x+4) - 3x + 6 + 6 = 2x² - 8x + 8 - 3x + 12 = 2x² - 11x + 20.