Write a system of equations with one linear equation and one quadratic equation for which (2, 6) is a solution.

1. OPEN ENDED Write a system of equations with one linear equation and one quadratic equation for which (2, 6) is a solution.

2. Writing in Math Use the information on page 306 to explain how the graph of y = x2 can be used to graph any quadratic function. Include a description of the effects produced by changing a, h, and k in the equation y = a(x – h)2 + k, and a comparison of the graph of y = x2 and the graph of y = a(x – h)2 + k using values of your own choosing for a, h, and k.

3. Writing in Math Use the information on page 314 to explain how you can find the time a trampolinist spends above a certain height. Include a quadratic inequality that describes the time the performer spends more than 10 feet above the ground, and two approaches to solving this quadratic inequality.

Please help, I’ve been stuck on these for days! Thanks.

GET READY for the Lesson
Cain Ideas
COncepts in Motion
Interactive Lab algebra2.com
y = x + 2
YNNI
Analyze quadratic
functions of the form
y = a(x – h)2+k.
Write a quadratic
function in the form
y = a(x – )2+ k.
A family of graphs is a group of graphs
that displays one or more similar
characteristics. The graph of y = x2 is
called the parent graph of the family of
quadratic functions.
y = (x-3)
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The graphs of other quadratic
functions such as y = x2 + 2 and
y = (x – 3)2 can be found by
transforming the graph of y = x2
rtex form
Axis of
(0,0)
x = 0
Analyze Quadratic Functions Each
function above can be written in the
form y = (x – h)2 + k, where (h, k) is
the vertex of the parabola and x = h is
its axis of symmetry. This is often
referred to as the vertex form of a
quadratic function.
Equation
y = x? or
y = (x –0)2+0
y = x2 + 2 or
y = (x – 02+2
y = (x – 3)2 or
y=(x – 3)2 + 0
(0,2)
X = 0
(3,0)
X = 3
Recall that a translation slides a figure
without changing its shape or size. As the values of h and k change, the
graph of y = a(x – h)2 + k is the graph of y = x2 translated:
• Th| units left if h is negative or |h| units right if h is positive, and
. |k| units up if k is positive or|k| units down if k is negative.
Graphing and Solving
Quadratic Inequalities
GET READY for the Lesson
Californian Jennifer Parilla is the only
athlete from the United States to
qualify for and compete in the
Olympic trampoline event.
Suppose the height h(t) in feet of a
trampolinist above the ground
during one bounce is modeled by
the quadratic function
h(t) = -16+2 +42+ + 3.75. We can
solve a quadratic inequality to
determine how long this performer
is more than a certain distance above
the ground.