Gr'10 Academic

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Gr.10 Academic

• 3.5 Quadratic Models Using Factored Form

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Example 1

• Thomas is watching fireworks from a secret
  admirer. The fireworks leave the ground at x 9
  and land at x -7. The point fireworks pass
  through point (2,63).

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a.) What is the axis of symmetry?
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b.) What is the equation of the parabola?
What are the zeroes?
What point do the fireworks travel through?
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c.) What are the coordinates of the vertex?

• y -1(x 9)(x 7)
• Axis of symmetry x 1
• So we substitute in to find y

Therefore the vertex is at (1, 64)
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d.) Sketch a graph of the parabola
Where does the graph not make sense?
Here it looks like the fireworks go through the
ground.
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Example 2

• Last month Sabrina sold 280 calculators at 20
  each. For every 0.50 that Sabrina increases her
  price, the number of sales will decrease by 5.
  What price will maximize Sabrinas revenue?

20.00 ? will sell 280
20.50 ? will sell 275
21.00 ? will sell 270
21.50 ? will sell 265
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Whats happening with the money?
(20 0.5x)
Whats happening with the number of calculators?
(280 5x)
Zeroes x -40 and x 56
So lets find the axis of symmetry
Now we need to find the vertex
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Take the axis of symmetry and substitute into the
original equation to find the y-coordinate of the
vertex.
So the vertex is at (8,5760)
So when Sabrina increases her price by 8
intervals, she will have a maximum revenue of
5760.
Money equation (20 0.5x)
20 0.5(8)
20 4
24
Therefore the maximum revenue is at 24