5.1:List the following words and give a mathematical definition in your own words on your wikispace. Remember, you may edit your definitions after we begin the unit.
quadratic - highest exponent is 2
vertex - Highest point
x-intercept - The point where the line crosses the x axis
y-intercept - The point where the line crosses the y axis
increasing - The y-value increases as the x-value increases.
decreasing - The y-value decreases as the x-value increases. maximum - Highest point minimum - Lowest point parabola - A curved, U-shaped graph that represents a quadratic equation
5.2:Summarize the similarities and differences between linear functions and quadratic functions. Discuss the graphs, the equations and the properties of each function.
Differences:
linear functions describes a line i.e 3x+2=y. Graphing that equation would result in a line. An example of a quadratic equation is x^2+3x+1=y. Graphing this equation would give you a U shaped graph; a parabola
5.5:
You and your friend are playing a game of tennis. Your friend throws the ball in the air, hitting the ball when it is 3 ft above the court with an initial velocity of 40 ft/sec. The height h(t) of the ball can be modeled by the function h(t) = -16t^2+40t+3, where t is the elapsed time in seconds after the dive.
Answer the following questions in your wikispace.
What shape does the path of the tennis ball make while traveling in the air.
Find h(1). Describe what h(1) means in the context of the problem
What is the y-intercept of h(t). In context, what does the y-intercept represent?
Identify the vertex. Describe in context what the x-coordinate of the vertex represents. Describe in context what the y-coordinate of the vertex represents.
What is the x-intercept(s) of h(t). In context what does the x-intercept(s) represent?
- Shape of the path is a curve.
- h (1) = 3 (initial height of the tennis ball).
- The y-intercept is ( 0,3) . At 0 seconds the ball was at 3 feet.
- Vertex = (1.25, 27.4) X coordinate of the vertex represents the the time where the ball will reach its highest point. Y coordinate is where the ball will reach its highest point.
- The x-intercept = (2.6, 0) X-intercept represents the time of when the ball drops.
5.1:List the following words and give a mathematical definition in your own words on your wikispace. Remember, you may edit your definitions after we begin the unit.
quadratic - highest exponent is 2
vertex - Highest point
x-intercept - The point where the line crosses the x axis
y-intercept - The point where the line crosses the y axis
increasing - The y-value increases as the x-value increases.
decreasing - The y-value decreases as the x-value increases.maximum - Highest point
minimum - Lowest point
parabola - A curved, U-shaped graph that represents a quadratic equation
5.2: Summarize the similarities and differences between linear functions and quadratic functions. Discuss the graphs, the equations and the properties of each function.
Differences:
linear functions describes a line i.e 3x+2=y. Graphing that equation would result in a line. An example of a quadratic equation is x^2+3x+1=y. Graphing this equation would give you a U shaped graph; a parabola
5.5:
You and your friend are playing a game of tennis. Your friend throws the ball in the air, hitting the ball when it is 3 ft above the court with an initial velocity of 40 ft/sec. The height h(t) of the ball can be modeled by the function h(t) = -16t^2+40t+3, where t is the elapsed time in seconds after the dive.
Answer the following questions in your wikispace.- Shape of the path is a curve.
- h (1) = 3 (initial height of the tennis ball).
- The y-intercept is ( 0,3) . At 0 seconds the ball was at 3 feet.
- Vertex = (1.25, 27.4) X coordinate of the vertex represents the the time where the ball will reach its highest point. Y coordinate is where the ball will reach its highest point.
- The x-intercept = (2.6, 0) X-intercept represents the time of when the ball drops.
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