Question

What is the equation of the axis of symmetry for the parabola y=1/2(x-3)^2+5 ?

Answer 1

X = 3

Let's start with the parabola y = x^2. It is obvious that the axis of symmetry is at x = 0.

Subtracting -3 from x before squaring gives y = (x-3)^2. Since any number squared is more than or equal to 0, we know that y=0 is still the lowest possible point on the parabola.

When y = 0, x = 3. From observation we can also see that the lowest point on the parabola is also where the axis of symmetry is. This means that the equation y = (x-3)^2 has axis of symmetry at x = 3.

Multiplying the right hand side by 1/2 compresses the graph vertically. You can see that this doesn't shift the axis of symmetry because you're compressing it along the axis of symmetry.

Adding 5 to the right side just moves the graph up by 5 units. Moving the graph up doesn't affect the axis of symmetry since only moving it left or right will affect it.

This gives you an axis of symmetry of x = 3.