Question

Instructions: Given the vertex of a quadratic function, find the axis

Answer 1

The axis of symmetry is x = 5.

In first place, every quadratic function can be expressed as follows:

f(x) = a*x² + b*x + c

where a, b and c are real numbers and a ≠ 0. This way of writing the quadratic function is called polynomial.

The graph of a quadratic function is a parabola. Every parabola is a symmetric curve with respect to a horizontal line called the axis of symmetry. That is, the axis of symmetry is an imaginary line that passes through the middle of the parabola and divides it into two halves that are mirror images of each other.

The point of intersection of the axis of symmetry with the parabola is called the vertex, and it divides the parabola into two branches. That is, the axis of symmetry always passes through the vertex of the parabola. The x-coordinate of the vertex is the equation of the axis of symmetry of the parabola.

Then, being the vertex of the quadratic function (5,7), where the vertex on the x-axis has a value of 5 and on the y-axis a value of 7, the axis of symmetry is x = 5.