the minimum value of y occurs at the origin.The y-axis is called the axis of symmetry of the parabola. This means that the y-value at, say x = 3, is the same as the y-value at x = −3. the graph is symmetrical about the y-axis.The basic parabola has a number of important properties. The path of a ball tossed under gravity at an angle to horizontal (roughly)įor the sake of convenience we will refer to the graph of y = x 2 as the basic parabola. Students will be familiar from earlier years with the graph of the function y = x 2 which they obtained by making up a table of values and plotting points. Their study in Year 10 gives an excellent introduction to important ideas that will be encountered in senior mathematics and beyond. The theory of these functions and their graphs enables us to solve simple maximisation/minimisation problems without having to resort to calculus. Quadratic functions frequently appears when solving a variety of problems.
Finding the vertex of a quadratic function how to#
The vertex of the parabola gives information regarding maximum height and combined with the symmetry of the curve also tells us how to find the horizontal range. The parabola also appears in physics as the path described by a ball thrown at an angle to the horizontal (ignoring air resistance). Since y = mx + b is an equation of degree one, the quadratic function, y = ax 2 + bx + c represents the next level of algebraic complexity. The graph of the function y = mx + b is a straight line and the graph of the quadratic function y = ax 2 + bx + c is a parabola. With the advent of coordinate geometry, the parabola arose naturally as the graph of a quadratic function. It arises from the dissection of an upright cone.
The parabola is a curve that was known and studied in antiquity. − Gilbert and Sullivan Pirates of Penzance. I understand equations, both the simple and quadratical. I’m very well acquainted too with matters mathematical, I know the kings of England, and I quote the fights historical,įrom Marathon to Waterloo, in order categorical I’ve information vegetable, animal, and mineral, I am the very model of a modern Major-General,
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