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Convert to vertex form: f(x)=4x^(2)-12 x+17

Convert to vertex form:\newlinef(x)=4x2−12x+17 f(x)=4 x^{2}-12 x+17

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Write a quadratic function in vertex formright chevron icon

Full solution

Q. Convert to vertex form:\newlinef(x)=4x2−12x+17 f(x)=4 x^{2}-12 x+17
  1. Identify vertex form: Identify the vertex form of a parabola, which is y=a(x−h)2+ky = a(x - h)^2 + k.
  2. Start with given equation: Start with the given equation f(x)=4x2−12x+17f(x) = 4x^2 - 12x + 17.
  3. Complete the square: To complete the square, take the coefficient of xx, which is −12-12, divide it by 22, and square it to get 3636.
  4. Add and subtract 3636: Add and subtract 3636 inside the equation to complete the square: f(x)=4(x2−12x+36)−36+17f(x) = 4(x^2 - 12x + 36) - 36 + 17.
  5. Factor the trinomial: Factor the trinomial: f(x)=4(x−6)2−36+17f(x) = 4(x - 6)^2 - 36 + 17.
  6. Combine the constants: Combine the constants: f(x)=4(x−6)2−19f(x) = 4(x - 6)^2 - 19.

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