Question

error analysis describe and correct the error in finding the axis of symmetry of the graph of $y = 3x^2 - 12x + 11$. $\boldsymbol{\times}$ $x = -\frac{b}{2a} = \frac{-12}{2(3)} = -2$ the axis of symmetry is $x = -2$.

Explanation:

Step1: Recall the formula for the axis of symmetry of a quadratic function \( y = ax^2 + bx + c \), which is \( x = -\frac{b}{2a} \).

In the given function \( y = 3x^2 - 12x + 11 \), \( a = 3 \) and \( b = -12 \).

Step2: Apply the formula correctly.

Substitute \( a = 3 \) and \( b = -12 \) into the formula \( x = -\frac{b}{2a} \). We get \( x = -\frac{-12}{2\times3} \).
Simplify the numerator and the denominator: \( -\frac{-12}{6}=\frac{12}{6} = 2 \).

Answer:

The error was in the sign of \( b \) when applying the axis of symmetry formula. The correct axis of symmetry is \( x = 2 \).