Integrated 2, Section 8-1
Teacher Notes: Parabola Solutions
Target 9 Level 2 I can solve quadratic equations using tables, graphs and the
quadratic formula.
Essential Questions
 What points help you find the solutions quadratic functions or equations?
 Which form of the quadratic equations can help you find each of the points?
Purpose:
Students identify points used in solutions.
Students identify the form of the equation that help them find the points.
Equation
vertex roots
factored form with roots r1 & r2
roots r1 & r2
y  a(x  r1 )(x  r2 )
2
vertex form
y  a(x  h)  k
standard form
y  ax 2  bx  c
(h,k)
y-intercept
a r1  r2 or
f 0
f 0
c or f 0
Task: Let students work with the graphs to solve the quadratic functions.
Launch:
What are the names key points in this graph?
What are the coordinates of those points?
Debrief: What types of points can you easily find with
equations written in each form?
a. vertex form: vertex
b. factored form: roots
c. standard form: y-intercept
Ticket Out:
During practice, a softball pitcher throws a ball whose
height can be modeled by the equation
h(t) = -16t2 + 24t +1, where h(t) = height in feet
and t = time in seconds.
How many seconds does it take the softball to reach
the maximum height? 0.75 seconds
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Integrated 2, Section 8-1
Parabola Solutions
Launch:
What are the names key points in this graph?
What are the coordinates of those points?
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Ticket Out
During practice, a softball pitcher throws a ball whose
height can be modeled by the equation
h(t) = -16t2 + 24t +1, where h(t) = height in feet and
t = time in seconds.
How many seconds does it take the softball to reach the
maximum height?
© Evergreen Public Schools 2/15/11
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Parabola Solutions
Integrated 2, Section 8-1
KEY
Target 9 Level 2 I can solve quadratic equations using tables, graphs and the
quadratic formula.
Solve. Show your work on your own paper, or on the back of this one.
Freemont Bridge
The equation represents the arch on the Freemont Bridge.
b(x) = -0.025x2 + 1.5x
1. How high is the highest point of the bridge above the
road?
22.5 feet – y-coordinate of the vertex
Kick a Soccer Ball
The height, h(t), in meters, t seconds after the kick is given
by the equation h(t)= -4.5t2 + 19.25t
2. What is the maximum height the soccer ball reaches?
20.6 feet – y-coordinate of the vertex
3. When does the soccer ball first hit the ground?
4.3 seconds – one of the roots
Pass the Football
In football, the height of the football reached during a pass
can be modeled by the equation
f(x) = -16x 2 + 28x + 6, where the height, f(x), is in feet and
the time, x, is in seconds.
4. How far above the ground was the quarterback holding
the football when he passed it?
6 feet – y-intercept
5. What type of point on the parabolas that you used to solve the four problems above?
1. vertex
2. vertex
3. roots
4. y-intercept
6. Debrief: What types of points can you easily find with equations written in each form?
a. vertex form: vertex
b. factored form: roots
c. standard form: y-intercept
© Evergreen Public Schools 2/15/11
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