Integrated 2, Section 8-1 Teacher Notes: Parabola Solutions

Target 9 Level 2 I can solve quadratic equations using tables, graphsand 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 / y-intercept
factored form with roots / roots / or
vertex form / /
standard form / c or

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?

  1. vertex form: vertex
  2. factored form: roots
  3. 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

Integrated 2, Section 8-1 Parabola Solutions

Launch:

What are the names key points in this graph?

What are the coordinates of those points?

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?


Integrated 2, Section 8-1Parabola Solutions

KEY

Target 9 Level 2 I can solve quadratic equations using tables, graphsand the quadratic formula.

Solve. Show your work on your own paper, or on the back of this one.

FreemontBridge
The equation represents the arch on the FreemontBridge.
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
  1. What is the maximum height the soccer ball reaches?
20.6 feet – y-coordinate of the vertex
  1. 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) = -16x2 + 28x + 6, where the height, f(x), is in feet and the time, x, is in seconds.
  1. How far above the ground was the quarterback holding the football when he passed it?
6 feet – y-intercept /
  1. What type of point on the parabolas that you used to solve the four problems above?

1. vertex2. vertex 3. roots4. y-intercept

  1. Debrief: What types of points can you easily find with equations written in each form?
  1. vertex form: vertex
  2. factored form: roots
  3. standard form: y-intercept

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