What is the axis of symmetry for the function f(x) = 3x² – 18x + 7?

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The axis of symmetry for a quadratic function in the standard form f(x) = ax² + bx + c can be calculated using the formula:

x = -b / (2a)

In your case, the quadratic function is:

f(x) = 3x² – 18x + 7

Here, the coefficients are:

  • a = 3
  • b = -18
  • c = 7

Now, let’s plug the values of a and b into the axis of symmetry formula:

x = -(-18) / (2 * 3)

This simplifies to:

x = 18 / 6 = 3

Therefore, the axis of symmetry for the function f(x) = 3x² – 18x + 7 is the vertical line:

x = 3

This means that the parabola opens upwards (since a is positive), and the line x = 3 sees the graph of the function mirrored on either side of it.

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