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Overview
Foundations of Mathematics and Pre-Calculus 10
3. Functions and relations: connecting data, graphs, and situations
3.12 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
BC Curriculum Aligned