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<p>The owner of a small clothing company wants to create a mathematical model for the company’s daily profit, pp, in dollars. based on the selling price, dd, in dollars, of the dresses made. The owner has noticed that the maximum daily profit the company has made is $1600. This occurred when the dresses were sold for $75 each. The owner also noticed that selling the dresses for $50 resulted in a profit of $1225. Using a quadratic relation to model this problem, create an equation for the company’s daily profit.</p>

<p>A model rocket is launched from the ground. After 20 s, the rocket reaches a maximum height of 2000 m. It lands on the ground after 40 s. </p><p>Explain how you could determine the equation of the relationship between the height of the rocket and time using two different strategies.</p>

<p>The cables of a suspension bridge form parabolas. If the minimum point of the centre cable is placed at the origin, determine an equation for each parabola. Describe the values of x for which each equation is valid.</p><img src="/qimages/771" />

<p>The cables of a suspension bridge form parabolas. If the minimum point of the centre cable is placed at the origin, determine an equation for each parabola. Describe the values of <code class='latex inline'>x</code> for which each equation is valid.</p><img src="/qimages/771" />

<p>A child kicks a soccer ball so that it barely clears a <code class='latex inline'>2 m</code> fence. The soccer ball lands 3 m from the fence. Determine the equation, in vertex form, of a quadratic relation that models the path of the ball.</p>

<p>The owner of a small clothing company wants to create a mathematical model for the company’s daily profit, <code class='latex inline'>p</code>, in dollars. based on the selling price, <code class='latex inline'>d</code>, in dollars, of the dresses made. The owner has noticed that the maximum daily profit the company has made is $1600. This occurred when the dresses were sold for <code class='latex inline'>\$75</code> each. The owner also noticed that selling the dresses for $50 resulted in a profit of <code class='latex inline'>\$1225</code>. Using a quadratic relation to model this problem, create an equation for the company’s daily profit.</p>

<p>The graph shows the path of a rocket fired from the deck of a barge in Lake Ontario at a Canada Day fireworks display. It is a parabola, where h is the height, in metres, of the rocket above the water and t is the time, in seconds.</p><img src="/qimages/772" />
<ul>
<li>When did the rocket reach its maximum height? Justify your answer.</li>
</ul>

<p>The graph shows the path of a rocket fired from the deck of a barge in Lake Ontario at a Canada Day fireworks display. It is a parabola, where h is the height, in metres, of the rocket above the water and t is the time, in seconds.</p><img src="/qimages/772" />
<ul>
<li>How high was the rocket above the water when it was set off? Explain your answer..</li>
</ul>

<p>The Lion’s Gate Bridge in Vancouver, British Columbia, is a suspension bridge that spans a distance of 1516 m. Large cables are attached to the tops of the towers, 50 m above the road. The road is suspended from the large cables by many smaller vertical cables. The smallest vertical cable measures about 2 m. Use this information to determine a quadratic model for the large cables.</p>

<p>The graph shows the path of a rocket fired from the deck of a barge in Lake Ontario at a Canada Day fireworks display. It is a parabola, where h is the height, in metres, of the rocket above the water and t is the time, in seconds.</p><img src="/qimages/772" />
<ul>
<li>What is the maximum height reached by the rocket? Justify your answer.</li>
</ul>

<p>A child kicks a soccer ball so that it barely clears a <code class='latex inline'>2 m</code> fence. The soccer ball lands 3 m from the fence. Determine the equation, in vertex form, of a quadratic relation that models the path of the ball.</p>

<p>The Lion’s Gate Bridge in Vancouver, British Columbia, is a suspension bridge that spans a distance of 1516 m. Large cables are attached to the tops of the towers, 50 m above the road. The road is suspended from the large cables by many smaller vertical cables. The smallest vertical cable measures about 2 m. Use this information to determine a quadratic model for the large cables.</p>

<p>The flight path of a firework is modelled by the relation <code class='latex inline'>h = -5(t -5)^2 + 127</code> where <code class='latex inline'>h</code> is the height, in metres, of the firework above the ground and t is the time, in seconds, since the firework was fired.</p><p><strong>(a)</strong> What is the maximum height reached by the firework? How many seconds after it was fired does the firework reach this height?</p><p><strong>(b)</strong> How high was the firework above the ground when it was fired?</p>