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Overview
Grade 11 Essential Mathematics (30S) - Half Course 3
Develop statistical reasoning
8. Solve problems that involve creating and interpreting graphs including bar graphs histograms line graphs and circle graphs
8.1 Finding the quadratic functions for given parabolas
Finding the Quadratic Function From a Graph
Given a parabola's vertex, roots, or a few points, learn which form to use and how to solve for the quadratic function that matches the graph.
What You'll Learn
A parabola's graph gives clues, like its vertex, roots, or plotted points, that determine which form of the quadratic function to build first
Vertex form \(y = a(x-h)^2+k\) is fastest when the vertex is visible on the graph
Intercept form \(y = a(x-p)(x-q)\) is fastest when the graph clearly crosses the x-axis at two points
When only scattered points are given, general form \(y = ax^2+bx+c\) with a system of equations always works
In every method, one extra point on the graph is needed to solve for the stretch factor \(a\)
What You'll Practice
1
Finding equations using vertex form with vertex and y-intercept
2
Writing quadratic functions from two x-intercepts using factored form
3
Solving for the leading coefficient using additional points on the parabola
4
Working with word problems describing vertex and x-intercept locations
Why This Matters
Finding quadratic functions from graphs is essential for modeling real-world situations where you observe parabolic patterns but need the equation. This skill connects graphical understanding to algebraic representation, preparing you for physics, engineering, and data analysis.
This Unit Includes
4 Video lessons
Practice exercises
Learning resources
Skills
Vertex Form
Factored Form
Quadratic Functions
Parabolas
Leading Coefficient
X-intercepts
Graphing
MB Curriculum Aligned