Identifying key features of quadratic functions worksheet answers

Three quadratic functions are graphed in the coordinate plane.

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Instead of looking at each function separately, we'll look at the characteristics individually and summarize our findings in a table at the end.

First, let's consider the direction of the parabolas. We can see that A and C open upward, and that B opens downward. The direction of a parabola determines whether the vertex is a minimum or a maximum. Thus, the vertices of A and C are minimums while the vertex of B is a maximum.

The vertex for each graph is found at the minimum or maximum of the function. For A, the vertex lies at (2,-4). Similarly, B's vertex lies at (-2,2), and C has its vertex at (0,-6).

The axis of symmetry is the vertical line that intersects the vertex. Therefore, the axis of symmetry for graph A is x=2, for B it's x=-2 and for C it is x=0.

The y-intercepts are found where the parabolas intercept the y-axis. A has the y-intercept y=0, B has y=-2 and C has y=-6. One of the options, y=4, does not coincide with any graph.

The zeros are found where the parabolas intercept the x-axis. Then, function A has zeros x=4 and x=0, which are two of the zeros given in the prompt. Neither function B nor function C has a zero at x=-6.

We summarize what we have learned about the characteristics of the three quadratic functions.

What are the key features of a quadratic function?

What are the 4 important features of a quadratic sketch?

Which graph shows the axis of symmetry for the function f X X 2 2 1?

Which of the following is the graph of a quadratic function?