Question

If the vertex of a parabola is (3,5), what is the symmetry

Answer 1

Answer:

axis of symmtery: x = 3 or h = 3

Step-by-step explanation:

The vertex (h, k) of a parabola is the point wherein the graph intersects the axis of symmetry—the imaginary straight line that bisects a parabola into two symmetrical parts, where x = h.

• In the standard form of quadratic equation, y =  ax² + bx + c, the equation of the axis of symmetry is:  $x = \frac{-b}{2a}$.

• In the vertex form of the quadratic equation, y = a(x - h)² + k, the equation of the axis of symmetry is:  $h = \frac{-b}{2a}$.

Regardless of whether the quadratic equation is in standard or vertex form, the x-coordinate (h) of the vertex determines the axis of symmtetry, hence, x = h.

Therefore, given that the vertex of a parabola is at point (3, 5), then it means that the axis of symmetry occurs at x = 3 or h = 3.