Question

a classmate found the axis of symmetry for the function (f(x)=3x^{2}-12x + 11) below: (x=-\frac{b}{2a}=\frac{-12}{2(3)}=-2). the axis of symmetry is (x = - 2). what mistake did your classmate make? and what is the correct axis of symmetry?

Explanation:

Step1: Identify coefficients

For the quadratic function $f(x)=ax^{2}+bx + c$, in $f(x)=3x^{2}-12x + 11$, $a = 3$ and $b=-12$.

Step2: Apply axis - of - symmetry formula

The formula for the axis of symmetry of a quadratic function is $x=-\frac{b}{2a}$. Substituting $a = 3$ and $b=-12$ into the formula, we get $x=-\frac{-12}{2\times3}$.

Step3: Calculate the value

$-\frac{-12}{2\times3}=\frac{12}{6}=2$. The classmate made a sign - error. They incorrectly took $b$ as $12$ instead of $- 12$ when substituting into the formula $x =-\frac{b}{2a}$.

Answer:

The classmate made a sign - error. The correct axis of symmetry is $x = 2$.