(5)

Did you know that parabolas like the one represented by the equation have a fascinating history? They were first studied by ancient Greek mathematicians, with the term “parabola” originating from the Greek word for “comparison”. The shape gained significance with the work of mathematicians like Apollonius and later in the development of calculus, where parabolas are used to describe various real-world phenomena, like the trajectory of projectiles!

When solving or graphing this quadratic function, a common mistake is overlooking the vertex and its implications. The vertex of this specific parabola is at the point (0, -9), meaning it opens upwards, touching its lowest point here. Always remember to check the direction of opening (determined by the coefficient of ) and the vertex’s position when analyzing the shape and symmetry of your parabola—this approach can save you from confusion and help you visualize it better!