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CH 3.1(PART I). Quadratic Functions. Lectures #12 and #
ย General and Standard forms of the equation of Quadratic Functions.
Definition.
f ( x ) = ax^2^ + bx + c , where a b c are real numbers a , , , โ 0
is called quadratic function (or second degree polynomial function) in general form.
2 f x = a x โ h + k is a standard form of the equation of a
quadratic function, ( h k , ) is the vertex.
ย Graphs of Quadratic Functions.
Problem #1.
Indicate how the graph of ( ) ( )
2 f x = x โ 3 โ 2 is
related to the graph of basic function f ( x ) = x^2. Sketch
the graph of ( ). State the Range of f.
2 y = x โ 3 โ 2
CH 3.1(PART I). Quadratic Functions. Lectures #12 and #
Problem #2.
Indicate how the graph of ( ) ( )
2 f x = โ x โ 3 โ 2 is
related to the graph of the basic function f ( x ) = x^2.
Sketch the graph of ( )
2 y = โ x โ 3 โ 2. State the Range of f.
Question. When a quadratic function has a maximum value? Minimum value?
CH 3.1(PART I). Quadratic Functions. Lectures #12 and #
Problem #3.
For ( )
2 3 2 4
f x = โโ^ x โ โโ โ โ โ
8 find the following:
a) Vertex.
b) Equation of the axis of symmetry.
c) y - intercept.
d) x - intercepts.
e) Maximum/minimum.
f) Range.
g) Using the info above sketch the graph of f ( x )
CH 3.1(PART I). Quadratic Functions. Lectures #12 and #
ย Conversion general form of a quadratic function into standard form (completing square procedure).
Problem #4.
Convert the function f ( x ) = โ 2 x^2 + 5 x โ 5 into standard
form ( ) ( )
2 f x = a x โ h + k.
ย Coordinates of the vertex when a quadratic function is given by an equation in general form.
For f ( x ) = ax^2 + bx + c , a โ 0 ,
the vertex is , 2 2
b b f a a
โ โ^ โ โ โโ
โ โ^ โ โ
Problem #5.
Find the vertex for y = โ 3 x^2 + 6 x โ 5.
State the Range for y = f ( x ).
CH 3.1(PART I). Quadratic Functions. Lectures #12 and #
ย Enclosing the Most Area with a Fence.
Problem #6.
A farmer with 2000 meters of fencing wants to
enclose a rectangular plot that borders on a straight
highway. If the farmer does not fence the side along
highway, what is the largest area that can be
enclosed?
Problem #7.
A rancher has 600 yards of fencing to put around a
rectangular field and then subdivide the field into two
identical plots by placing a fence parallel to field's
shorter sides. Find the dimensions that maximize
enclosed area. What is the maximum area?
CH 3.1(PART I). Quadratic Functions. Lectures #12 and #
Problem #8.
Shannise Cole makes and sell candy. She has found
that the cost per box for making x boxes of candy is
given by
2
C x = x โ 40 x + 405
a) How much does it cost per box to make 15 boxes?
b) What point on the graph corresponds to the
number of boxes that will make the cost per box
as small as possible?
c) How many boxes should she make in order to keep
the cost per box at a minimum?
What is the minimum cost per box?
Problem #9.
A bullet is fired upward from the ground level.
Its height above the ground (in feet) at time t seconds
is given by
2
H = โ 16 t + 100 t
Find the maximum height of the bullet and the time
at which it hits the ground.
