Question

Rewrite the quadratic function in standard form. f(x) = x² - 18x + 85

Answer 1

To rewrite the quadratic function f(x) = x² - 18x + 85 in standard form, complete the square to find the vertex form, resulting in f(x) = (x - 9)² + 4 with the vertex at (9, 4).

Step-by-step explanation:

To rewrite the quadratic function f(x) = x² - 18x + 85 in standard form, we look for the vertex form of a quadratic equation, which is given by:

f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

To complete the square:

1. Divide the coefficient of the x term by 2, which gives us -18/2 = -9.
2. Square this result, which gives us 81.
3. Add and subtract this squared number inside the quadratic expression: f(x) = (x² - 18x + 81) - 81 + 85.
4. We can now rewrite this as a perfect square trinomial: f(x) = (x - 9)² - 81 + 85.
5. Simplify the constant terms to get the standard form: f(x) = (x - 9)² + 4.

This is the quadratic function in standard form, with the vertex of the parabola at (9, 4).

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