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Substitute (x-1) into the function f(x) = 3x² − 2x + 5.

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Graph of f(x) = 3x² − 2x + 5

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Key points of f(x) = 3x² − 2x + 5
Pointxy
y-intercept05
Minimum0.334.67

Step 1: Substitute (x−1)(x-1) into the function f(x)=3x2−2x+5f(x) = 3x^2 - 2x + 5.

f(x−1)=3(x−1)2−2(x−1)+5f(x-1) = 3(x-1)^2 - 2(x-1) + 5

Step 2: Expand the squared term and distribute.

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

Step 3: Combine like terms.

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