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# The Key Features Of A Quadratic Graph

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on 28 October 2015

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#### Transcript of The Key Features Of A Quadratic Graph

The Key Features Of A Quadratic Graph
Key Features Of A Quadratic Graph
There are many key features in a quadratic graph such as the zeroes (x-intercepts, also known as the roots), y-intercept, axis of symmetry, and the vertex. We will be taking a look at these four features in this presentation.
The Zeroes
The zeroes, also known as the roots, are the x-intercepts of the parabola. A parabola can either have no zeroes, two zeroes, or one zero, but only if the vertex is on the x-intercept. The zeroes form when both sides of the parabola intersect the x-axis. In most cases, a parabola will have two zeroes. If a parabola has no zeroes, this means that the whole relationship is either under or over the x-axis. If there is only one zero in the parabola however, that means that the vertex (corner) is dead on the x-axis.
The Y-intercept
The y-intercept of a parabola is where the line intersects in the y-axis. No matter what, a parabola will always intersect the y-axis. If there is no y-intercept on a line, then you know it is not a parabola.
The Axis Of Symmetry
The axis of symmetry is the halfway point of a parabola. It splits up the parabola evenly on each side. The axis of symmetry always goes up vertically and the equation looks like this: x=a, where a is the point on the x-axis where the axis of symmetry intersects it. If there is no way to fit an axis of symmetry and the line is not symmetrical on the graph, then that means the relationship is not a parabola.
A quadratic graph has an equation that has a degree of 2 (meaning that the highest exponent in the equation is 2). The equation would look like this in standard form: y=ax +bx+c. When you see this relation on graph, it will look like a U shape. The U shape can either be facing upwards or downwards depending on if the a value is a negative or a positive. Quadratic relations can be used for many situations such as the height and time of an object being thrown. The height will increase at first and later, it will decrease. A quadratic graph can also be called a parabola. But what are the key features of a quadratic graph, you may ask? Let's take a look in what...
No zeroes
One zero
Two zeroes
The Vertex
The vertex is the corner of the parabola, also known as the point on the line where it bends. The vertex is either the highest point of the parabola, or the lowest, on the graph. The vertex is usually determined by using the axis of symmetry to replace the x value in an equation and solving for y to acquire the coordinates with both, x and y. The vertex is also what causes the U shape of a parabola. If you see that a relationship does not have a vertex or is not in a U shape, that means that it is not a parabola.