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Describing Properties of a Parabola From Equation

Let’s start by graphing y equals x squared.

We’ll use this table of values, and plot them on the number plane. What are the main features of this graph?

The parabola is a smooth curve without any sharp points. It has a minimum value of a turning point called the vertex. As we can see the minimum value of this parabola is at zero, zero.

That is this parabola exists only above the origin. The parabola is symmetrical about a central line called the axis of symmetry. In this case, the axis of symmetry is the Y-axis. This parabola is also an even function. We can describe this function as f over x equals x squared. When f of x equals f of -x we have an even function.

For example, if we calculate the function of three which is three squared, we get nine. And if we calculate the function of minus three which is minus three squared, we also get nine.

Lastly, the curve is described as concave up. In other words, it looks like we could fill it with water.

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