Quadratic Functions: Goals, Problems, and Practice - Prof. Robert Buskirk, Study notes of Algebra

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Section 2-3: Quadratic Functions

R. D. Buskirk Eastern Kentucky University

Fall 2008

Goals You will learn (review) to^ •^ recognize and use geometric properties of quadratic functions;^ •^ use different forms of equation for quadratic functions (where^ a, b, c, h, k

∈^ R^ and

a^6 = 0

f^ (x) =

(^2) ax+ bx^ +^

c^

general form

f^ (x) =

a^ (x^ −

(^2) h)+ k,^ h

=^ −^

b, 2 a

(^4) k = ac^ −^ b

2 =^ f 4 a

(b^ −^2 a

vertex form

-^ algebraically transform one form of the equation to the other form,including

completing the square

-^ algebraically find the

vertex

,^ axis of symmetry

Practice, practice, practice, practice,... Problem 1

Sketch the graph of

y^ =^ −

(x^ + 3)

2 + 2^ without using a

calculator.

Problem 2

Complete the square and find the vertex form of the quadratic function. Then find the vertex and axis.(a)^ f^ (

x) =^ x

2 −^5 x

Problem 3

Find the vertex using the vertex formula, then graph the function showing the vertex, axis and

y-intercept:

f^ (x) =

(^2) − 2 x

• 5x^ + 3

Problem 4

Find the equation of the quadratic function whose graph has vertex

(−^2 ,^ 11)

and a point

(3,^ 5)

Problem 6

A coyote falls from a cliff and smacks into the desert canyon below^

3 .1 sec

later: we see the dust cloud. How high was the cliff? Assume that flailing arms and fur produce no aerodynamic drag. Furtherassume that the coyote does not stop in midair, etc.

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