Question:
<p>If the vertex of the parabola y = x<sup>2</sup> - 8x + c lies on x-axis, then the value of c is</p>
<p style="display:inline">16</p>
<p style="display:inline">4</p>
<p style="display:inline">-16</p>
<p style="display:inline">-4</p>
Step-by-Step Solution
Key Concept: The vertex of a parabola lies on the x-axis if and only if the y-coordinate of the vertex is zero, which corresponds to the quadratic being a perfect square.
<p>The given equation can be written as (x - 4)<sup>2</sup> = y - (c - 16). Therefore the vertex of the parabola is (4, c - 16). Since, the point lies on x-axis.<br />
<span class="math-tex">\(\Rightarrow\)</span> c - 16 = 0<br />
<span class="math-tex">\(\Rightarrow\)</span> c = 16</p>
Correct Answer: A