Definition--Quadratics Concepts--Minimum
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Algebra >> Quadratic Functions and Equations >> Quadratic Equations and Functions

Definition--Quadratics Concepts--Minimum

Minimum

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Topic

Quadratics Concepts

Definition

The minimum of a quadratic function is the lowest point on its graph, occurring at the vertex when the parabola opens upward.

Description

The minimum of a quadratic function is a key concept in analyzing the behavior of parabolas. When a quadratic function is in the form 

f(x) = ax2 + bx + c 

with a > 0, the parabola opens upward, and the vertex represents the minimum point. This minimum value is crucial in optimization problems, where determining the lowest value of a function is necessary, such as minimizing cost or error. In math education, understanding the minimum of quadratic functions helps students analyze and graph parabolas, solve real-world problems, and comprehend the significance of the vertex in determining function behavior. 

An example of finding the minimum is in the function 

f(x) = x2 − 4x + 4

where the vertex and minimum point is ( 2 , 0 ) (2,0).

For a complete collection of terms related to Quadratic Expressions, Functions, and Equations click on this link: Quadratics Collection

Common Core Standards CCSS.MATH.CONTENT.HSN.CN.C.7, CCSS.MATH.CONTENT.HSA.SSE.B.3.B, CCSS.MATH.CONTENT.HSA.REI.B.4.A, CCSS.MATH.CONTENT.HSF.IF.C.8.A
Grade Range 6 - 10
Curriculum Nodes Algebra
    • Quadratic Functions and Equations
        • Quadratic Equations and Functions
Copyright Year 2021
Keywords quadratic functions, quadratic equations, quadratic formula, definitions, glossary terms