### Quadratic equations: Parabola

### Parabola

Graph

The graph of a quadratic \[y=\blue ax^2+\green bx+\purple c\] is called a **parabola.**

If #\blue a \gt 0# the graph is an **upward opening parabola.**

If #\blue a \lt 0# the graph is a **downward opening parabola.**

An upward opening parabola has a minimum and downward opening parabola has a maximum. In both cases, this point is referred to as the **vertex **of the graph.

The parabola is symmetrical about the vertical line through the top of the graph. Such a line is also called a #\orange{\textbf{line of symmetry}}#.

geogebra picture

Take a look at the formula #y=3\cdot x^2+45\cdot x+168#. Does the point #\rv{3, 323}# lie on the graph of this formula?

No

We substitute #x=3# in the formula. This is done in the following way:

\[y=3\cdot (3)^2+45\cdot (3)+168=330\]

Hence #\rv{3, 323}# does not lie on the graph.

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