Based on my analysis of the image, I can see that this is a worksheet with 8 different graphs of parabolas, each accompanied by information about the function. The task appears to be matching or analyzing these graphs with their corresponding properties.
Looking at the graphs and their associated information, I can identify the following patterns:
1.
Top-left graph: Parabola opening downward with vertex at (-1, 4), domain (-∞, ∞), range (-∞, 4], x-intercepts at -3 and 1, y-intercept at 3, and a negative a-value.
2.
Top-right graph: Parabola opening downward with vertex at (1, 4), domain (-∞, ∞), range (-∞, 4], x-intercepts at -1 and 3, y-intercept at 3, and a negative a-value.
3.
Middle-left graph: Parabola opening upward with vertex at (1, -4), domain (-∞, ∞), range [-4, ∞), x-intercepts at -1 and 3, y-intercept at -3, and a positive a-value.
4.
Middle-right graph: Parabola opening upward with vertex at (-1, -4), domain (-∞, ∞), range [-4, ∞), x-intercepts at -3 and 1, y-intercept at -3, and a positive a-value.
The remaining graphs (bottom row) follow similar patterns, showing parabolas with different vertices, directions of opening, and intercepts.
The task likely involves:
- Identifying the vertex, domain, range, intercepts, and the sign of the leading coefficient (a-value) for each parabola.
- Understanding how the position of the vertex and the direction of opening affect these properties.
- Possibly matching graphs with their equations or identifying transformations from a parent function.
To solve this problem completely, one would need to analyze each graph systematically, noting the key features (vertex, direction of opening, intercepts) and relating them to the standard form of a quadratic function: f(x) = a(x-h)² + k, where (h,k) is the vertex and 'a' determines the direction and width of the parabola.
The solution would involve verifying that the given information for each graph matches the visual representation and understanding the relationships between the algebraic properties and the graphical representation of quadratic functions.
Parent Tip: Review the logic above to help your child master the concept of characteristics of quadratic functions worksheet answers.
