Math Problem Statement

answer

Investigating All Three Forms Card Sort - Match graphs and equations for quadratic functions.

Solution

I see the uploaded image of the worksheet. To help, I'll extract and analyze the equations and graphs for matching or solving the task of "Investigating All Three Forms Card Sort." Let me provide insights.

Observations:

The worksheet appears to compare quadratic equations and their graphs across three forms:

  1. Standard Form: ax2+bx+cax^2 + bx + c
  2. Factored Form: a(xr1)(xr2)a(x - r_1)(x - r_2)
  3. Vertex Form: a(xh)2+ka(x - h)^2 + k

Quadratic graphs are matched with equations in various forms. I’ll start by analyzing each.

Would you like me to:

  1. Match equations to graphs step-by-step?
  2. Explain the key features (vertex, axis of symmetry, roots) for each equation and graph?
  3. Help solve specific parts of the worksheet? Let me know your focus!

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Functions
Graphing
Forms of Quadratic Equations

Formulas

Standard Form: y = ax^2 + bx + c
Factored Form: y = a(x - r1)(x - r2)
Vertex Form: y = a(x - h)^2 + k

Theorems

Roots of Quadratic Equations
Vertex and Axis of Symmetry
Factoring and Completing the Square

Suitable Grade Level

Grades 8-10