What is the equation of the line of symmetry for y = x^2 + 4x - 5?

Question

I have a feeling I'm just making this more difficult than it really is.

Answer 1

Well, a parabola is symmetrical about the line that goes through its turning point right? So what you need to do is find the x coordinate of the turning point.

y = x^2 + 4x - 5
y' = 2x+4
2x+4 = 0
x = -2

Therefore, the equation of the line of symmetry is x=-2

Answer 2

You didn't say if you are in calculus or precalculus. If it is the former, someone has already answered your question.

If you are in precalculus you need to find the vertex of the parabola. To do that complete the square.

y = x² + 4x - 5
y + 5 = x² + 4x
y + 5 + 4 = x² + 4x + 4
y + 9 = (x + 2)²

The vertex of the parabola is (-2, -9).

The line of symmetry runs thru the vertex and is vertical like the parabola. Therefore the line of symmetry is:

x = -2