Question

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

Answer 1

x = 3

Step-by-step 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{ = -}(b)/(2a)`

We have that:

b = -6

a = 1

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

That is the axis of symmetry of the equation.