<p>Question 16 on page 475 in the Blue book!</p>
<p>Let the function h be defined by h(x) = 14 + (x^2)/4. If h(2m) = 9m, what is one possible value of m?</p>
<p>set up the equation: 14 + ((2m)^2)/4 = 9m</p>
<p>14 + (4m^2)/4 = 9m</p>
<p>the 4 in the denominator of the fraction cancels:</p>
<p>14 + m^2 = 9m</p>
<p>m^2 - 9m +14 = 0</p>
<p>factor the trinomial</p>
<p>(m - 7)(m - 2) = 0</p>
<p>m = 7 or m = 2</p>
<p>simple:</p>
<p>assign 2m to the x in the given equation.</p>
<p>14 + (2m/4)power2 = 9m (given)</p>
<p>simplify:</p>
<p>14 + (4m2/16) = 9m</p>
<p>simplify the left side:</p>
<p>(56 + 4m2)/ 16</p>
<p>{4(14 + m2)/16} = 9m</p>
<p>so:</p>
<p>m2 - 9m + 14 </p>
<p>factor it:</p>
<p>(m - 7) (m - 2)</p>
<p>so m could be 7 or 2.</p>