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F-BF.1.a Warmup M2-014-A04-V03

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

From the plotted vertex \((0,-4)\), write \(f(x)=a(x-0)^{2}-4\). Use \((3,14)\) to find \(a\), simplify the model, and check that it retains the vertex and passes through the point.

Source graph showing vertex (0,−4) and additional point (3,14); 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