writing equations vertex form quiz.notebook
April 06, 2010
Writing Equations in Vertex Form:
general equation
y = a(x ­ h)2 + k
where: (h, k) are the coordinates of the VERTEX
"a" determines direction of OPENING
whether STRETCHED or COMPRESSED
To determine "a" ­­ the coefficient of the x2 term...
1) first step of the Step Pattern from the Vertex
2) if the first step is difficult to determine,substitute a point from the graph into the general equation in vertex form, and solve for "a"
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writing equations vertex form quiz.notebook
April 06, 2010
Quiz: modelling equations in Vertex Form
Scenario: A projectile was launched from an initial position on the Height above ground in meters
ground. The projectile travelled in a parabolic path. It landed 16 m away from its initial position and reached a maximum height of 6 m. a) What is the position of the maximum height (vertex coordinates)
b) Sketch the graph of the path of the projectile using the vertex and the 2 other known positions
c) Write a relation to model the motion of the projectile in Vertex Form. d) Using your equation, determine the height above the ground of the projectile when it is 4m away from its inital position? Show all your work.
Horizontal distance travelled in meters
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writing equations vertex form quiz.notebook
April 06, 2010
What are the 2 possible solutions for x given:
x2 = 25
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writing equations vertex form quiz.notebook
April 06, 2010
Solve the following equation for 'd' (distance) given an initial height "h" of 0
h = ­2 ( d ­3)2 +12
show both possible solutions
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April 06, 2010
height above ground
writing equations vertex form quiz.notebook
distance
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writing equations vertex form quiz.notebook
April 06, 2010
What are the horizontal distances travelled when the projectile is at a height of 4 m. Show both solutions.
What is the width of the parabola at a height "h" of 4
h = ­2 ( d ­3)2 +12
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writing equations vertex form quiz.notebook
April 06, 2010
CONSOLIDATE YOUR LEARNING:
1. Determine the quadratic equation for the graph below, and answer the following questions:
a) what are the coordinates of the
vertex
b) what is the direction of the opeining
c) determine the step pattern and value of "a" ­­coefficient of x2
d)write the equation in vertex form
represented by the graph
2. Determine the equation in vertex form, represented by the graph below, and answer the following questions;
a) what are the coordinates of the vertex
b) identify the coordinates of another point that is on the graph
c) using this point, and the vertex:
determine the value of "a" y = a(x ­ h)2 +k
d) Write the equation for the graph 7
writing equations vertex form quiz.notebook
April 06, 2010
3. The equation of a quadratic relation is : y = ­0.75(x­3)2 +5
Solve for the 2 values of x when y is 2. Show all your work.
4. A construction worker drops a wrench. Its fall is modelled by the relation, h = ­4.9 t2 + 342 , where h is height above ground in metres and t is time in seconds.
a) how far above the ground was the wrench when it was dropped? t = 0
b) how far has the wrench fallen after 5 seconds?
c) When will the wrench hit the ground? (when h=0, solve for t)
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