Example

Evaluating the Polynomial Function f(x)=5x2−8x+4f(x) = 5x^2 - 8x + 4

To evaluate the polynomial function f(x)=5x2−8x+4f(x) = 5x^2 - 8x + 4 for specific values, substitute the value for the independent variable xx and simplify using the order of operations:

  • Evaluate f(4)f(4): Substitute 44 for xx to obtain f(4)=5(4)2−8(4)+4f(4) = 5(4)^2 - 8(4) + 4. Simplifying the exponent gives 5(16)−32+45(16) - 32 + 4. Multiply to get 80−32+480 - 32 + 4, and simplify to find f(4)=52f(4) = 52.
  • Evaluate f(−2)f(-2): Substitute −2-2 for xx to obtain f(−2)=5(−2)2−8(−2)+4f(-2) = 5(-2)^2 - 8(-2) + 4. Simplifying the exponent gives 5(4)−(−16)+45(4) - (-16) + 4. Multiply to get 20+16+420 + 16 + 4, and simplify to find f(−2)=40f(-2) = 40.
  • Evaluate f(0)f(0): Substitute 00 for xx to obtain f(0)=5(0)2−8(0)+4f(0) = 5(0)^2 - 8(0) + 4. Simplifying the exponent gives 5(0)−0+45(0) - 0 + 4, which simplifies to f(0)=4f(0) = 4.

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Updated 2026-05-12

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