<p>The following diagram shows part of the graph of a quadratic function \(f\).</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1788162562714-09q1z3rp6voq.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3ODgxNjI1NjI3MTQtMDlxMXozcnA2dm9xLnBuZyIsInNjb3BlIjoiZG93bmxvYWQiLCJpYXQiOjE3ODgxNzk1NDgsImV4cCI6MTc4ODE3OTg0OH0.JkkbvayIaPrl7RBMgyuG2Qp_kRHLdYrDSCMBdj1WnNo" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<p>The \(x\)-intercepts are at \( (-4,0)\) and \( (6,0) \) and the \(y\)-intercept is at \((0,240)\).</p>
<ol class="abc-list"><li data-list-item-id="item-1788162614036-80upe43tv" data-list-item-path="item-1788162614036-80upe43tv"><div class="list-item-paragraph"><p>Write down \(f(x)\) in the form \(f(x) = -10(x - p)(x - q)\).</p><span class="inline-marks">[2]</span></div></li><li data-list-item-id="item-1788162614946-jcvxqzij3" data-list-item-path="item-1788162614946-jcvxqzij3"><div class="list-item-paragraph"><p>Find another expression for \(f(x)\) in the form \(f(x) = -10(x - h)^2 + k\).</p><span class="inline-marks">[4]</span></div></li><li data-list-item-id="item-1788162615578-ohnzh85gf" data-list-item-path="item-1788162615578-ohnzh85gf"><div class="list-item-paragraph"><p>Show that \(f(x)\) can also be written in the form \(f(x) = 240 + 20x - 10x^2\).</p><span class="inline-marks">[2]</span></div></li></ol>
<p>A particle moves along a straight line so that its velocity, \(\mathrm{v}\) m s\(^{-1}\), at time \(t\) seconds is given by \(\mathrm{v} = 240 + 20t - 10t^2\), for&nbsp;\(0 \leq t \leq6\).</p>
<ol class="abc-list" start="4"><li data-list-item-id="item-1788162804280-y76l6hme5" data-list-item-path="item-1788162804280-y76l6hme5"><ol class="i-list"><li data-list-item-id="subitem-1788162807199-w2fwrerde" data-list-item-path="item-1788162804280-y76l6hme5/subitem-1788162807199-w2fwrerde"><div class="list-item-paragraph"><p>Find the value of \(t\) when the speed of the particle is greatest.</p></div></li><li data-list-item-id="subitem-1788162807815-bcm4yb9l3" data-list-item-path="item-1788162804280-y76l6hme5/subitem-1788162807815-bcm4yb9l3"><div class="list-item-paragraph"><p>Find the acceleration of the particle when its speed is zero.</p><span class="inline-marks">[7]</span></div></li></ol></li></ol>

The following diagram shows part of the graph of a quadratic function \(f\).

The \(x\)-intercepts are at \( (-4,0)\) and \( (6,0) \) and the \(y\)-intercept is at \((0,240)\).

<p>Write down \(f(x)\) in the form \(f(x) = -10(x - p)(x - q)\).</p>

<p>Find another expression for \(f(x)\) in the form \(f(x) = -10(x - h)^2 + k\).</p>

<p>Show that \(f(x)\) can also be written in the form \(f(x) = 240 + 20x - 10x^2\).</p>

A particle moves along a straight line so that its velocity, \(\mathrm{v}\) m s\(^{-1}\), at time \(t\) seconds is given by \(\mathrm{v} = 240 + 20t - 10t^2\), for \(0 \leq t \leq6\).

Functions

International Baccalaureate Mathematics: Applications and Interpretation Standard Level