Three quadratic functions are graphed in the coordinate plane. Show expand_more 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 characteristics of quadratic functions?Three properties that are universal to all quadratic functions: 1) The graph of a quadratic function is always a parabola that either opens upward or downward (end behavior); 2) The domain of a quadratic function is all real numbers; and 3) The vertex is the lowest point when the parabola opens upwards; while the ...
How do you identify the characteristics of a quadratic function from a graph?Characteristics of Parabolas
The graph of a quadratic function is a U-shaped curve called a parabola. One important feature of the graph is that it has an extreme point, called the vertex. If the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function.
How do you describe a quadratic function?A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in "width" or "steepness", but they all have the same basic "U" shape.
What are the 4 important features of a quadratic sketch?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.
|
Characteristics of quadratic functions worksheet answer key
Copyright © 2024 chuyencu Inc.
