Question

4/12 what is the axis of symmetry for f(x)=4(x - 2)^2+3

Explanation:

Step1: Expand the quadratic function

First, expand \(f(x)=4(x - 2)^2+3\). Using the formula \((a - b)^2=a^{2}-2ab + b^{2}\), we have \(f(x)=4(x^{2}-4x + 4)+3=4x^{2}-16x+16 + 3=4x^{2}-16x+19\).

Step2: Recall the formula for the axis - of - symmetry of a quadratic function

For a quadratic function in the form \(y = ax^{2}+bx + c\), the axis of symmetry is given by the formula \(x=-\frac{b}{2a}\). In \(y = 4x^{2}-16x+19\), \(a = 4\) and \(b=-16\).

Step3: Calculate the axis of symmetry

Substitute \(a = 4\) and \(b=-16\) into the formula \(x=-\frac{b}{2a}\), we get \(x=-\frac{-16}{2\times4}=\frac{16}{8}=2\).

Answer:

\(x = 2\)