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F-BF.1.a Warmup M2-014-A04-V04

Build quadratic and exponential functions from context using explicit formulas, recursive processes, or calculation steps.

Build a quadratic function in vertex form from a vertex and one point

Problem

The graph gives vertex \((1,4)\) and point \((3,0)\). Put the vertex into \(f(x)=a(x-h)^{2}+k\), substitute the second point, solve for \(a\), and verify both graph features in the final function.

Source graph showing vertex (1,4) and additional point (3,0); no completed quadratic or scale factor is shown. Open full size
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Four variants of this problem type
Curriculum context
Course
Math II
Standard
F-BF.1.a
Category
Functions
Domain
Building Functions
Objective
Build quadratic and exponential functions from context using explicit formulas, recursive processes, or calculation steps.
Problem type
Build a quadratic function in vertex form from a vertex and one point