Identify the axis of symmetry of the quadratic function 𝑓 of 𝑥 equals 𝑥 squared minus one.
We’ve been given the equation of a function and the graph of this function. Recall that the axis of symmetry is a line through a shape about which each side is a mirror image of the other side. And the shape of a quadratic function is a parabola. Sometimes we can find the line that is the axis of symmetry visually. But for the sake of accuracy, when we know the function, we should use that form. Our function 𝑓 of 𝑥 equals 𝑥 squared minus one can be compared to the standard form for the quadratic function 𝑦 equals 𝑎𝑥 squared plus 𝑏𝑥 plus 𝑐.
For functions in standard form, the axis of symmetry is located at 𝑥 equals negative 𝑏 over two 𝑎. Our function 𝑓 of 𝑥 equals 𝑥 squared minus one has values 𝑎 equals one, 𝑏 equals zero, and 𝑐 equals negative one. Our axis of symmetry would be located at negative 𝑏 over two 𝑎. In this case, we have zero as our 𝑏-value, and therefore the line that is the axis of symmetry is located at 𝑥 equals zero. The 𝑦-axis is the line of symmetry for this parabola.