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Identifying The Extreme Values Of Quadratic Functions Worksheet With Answer Key - Math 11011 College Algebra, Kent State University

MATH 11011

IDENTIFYING THE EXTREME VALUES

KSU

OF QUADRATIC FUNCTIONS

Deﬁnitions:

Quadratic function: is a function that can be written in the form

f (x) = ax

+ bx + c

where a, b, and c are real numbers and a = 0.

Parabola: The graph of a squaring function is called a parabola. It is a U-shaped graph.

Vertex of a parabola: The point on the parabola where the graph changes direction. It is the

lowest point if a > 0, and it is the highest point if a < 0.

Standard form of a quadratic function: A quadratic function f (x) = ax

+ bx + c can be

expressed in the standard form

f (x) = a(x

+ k

by completing the square.

Important Properties:

Extreme values of a quadratic function: Consider the quadratic function f (x) = a(x

+ k.

– If a > 0, then the parabola opens up. Therefore, the minimum value of f occurs at x = h

and its value is f (h) = k.

– If a < 0, the parabola opens down. Therefore, the maximum value of f occurs at x = h and

its value is f (h) = k.

Vertex Formula: Given the quadratic f (x) = ax

+ bx + c, the vertex is found using

, f

Common Mistakes to Avoid:

Notice that the maximum or minimum value is the y coordinate of the parabola’s vertex. Do not

record the extreme value as the x coordinate.

Determining whether the y coordinate of the vertex is a maximum or minimum depends on whether

a is positive or negative. It does NOT depend on whether the y coordinate is positive or negative.

Identifying The Extreme Values Of Quadratic Functions Worksheet With Answer Key - Math 11011 College Algebra, Kent State University