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Here are two equations that define quadratic functions.
The graph of
Find the coordinates of another point on the graph of
Priya says, "Once I know that the vertex is
Complete the table, and then explain how Priya might have reasoned about whether the vertex is the minimum or maximum.
| 3 | 4 | 5 | |
| 10 |
Not surprisingly, vertex form is especially helpful for finding the vertex of a graph of a quadratic function. For example, we can tell that the function,
We also noticed that, when the squared expression
Parabola in x y plane, origin O. X axis 0 to 6, by 1’s. Y axis 0 to 10, by 2s. Parabola opens upward with vertex at 3 comma 1. Left side of parabola crosses the y axis at 10.
But why does function
Here is one way to explain it: When
This table shows some values of the function for some values of
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | |
| 10 | 5 | 2 | 1 | 2 | 5 | 10 |
The squared term sometimes has a negative coefficient, for instance in
Remember that we can find the
Parabola in x y plane, origin O. X axis negative 4 to 1, by 1’s. Y axis negative 8 to 2, by 2s. Parabola opens upward with vertex at negative 1 comma negative 5. Other points on the parabola given are negative 2 comma negative 4 and 0 comma negative 4.