Question

y = (x - 3)^2 Axis of symmetry? y=0 y=3 x=3 x=-3

Answer 1

ANSWER

x = 3

EXPLANATION

We want to find the axis of symmetry of the quadratic equation given.

To do that, we have to first write the equation in the general form of a quadratic equation:

$y=ax^2\text{ + bx + c}$

The given equation is:

$\begin{gathered} y=(x-3)^2 \\ \text{Expand it:} \\ y=\text{ (x - 3)(x - 3)} \\ y=x^2\text{ - 3x - 3x + 9} \\ y=x^2\text{ - 6x + 9} \end{gathered}$

The axis of symmetry of a quadratic equation can be found as:

$x\text{ = -}\frac{b}{2a}$

We have that:

b = -6

a = 1

$\begin{gathered} \Rightarrow\text{ x = }\frac{-(-6)}{2}\text{ = }\frac{6}{2} \\ x\text{ = 3} \end{gathered}$

That is the axis of symmetry of the equation.