nahin.ipynb

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    "He's shown that the function can be written as\n",
    "\n",
    "$$ a[(x-p)^2 + q^2] $$\n",
    "\n",
    "So that shows it's the graph of $y = x^2$, shifted to the right by $p$, shifted up by $q^2$ and then scaled by a factor of $a$. So, the minimum is at $p$.\n",
    "\n",
    "Now the task is similarly to \"read off\" the value of $q$. Multiplying out, it's\n",
    "\n",
    "$$ a(x-p)^2 + aq^2 $$\n",
    "\n",
    "I *think* he looks at this and says \"if $x-p = q$ then the whole thing is going to be $2aq^2$\". So $q$ is the value of $x$ where the function is equal to $2aq^2$, minus $p$.\n",
    "\n",
    "\n",
    "Maybe there are other equivalent ways to \"read off\" the value of $q$ from the graph, in the same way that in geometry problems a line/chord/angle/whatever of the same value may appear in multiple places?\n",
    "\n",
    "\n",
    "Also, could he have said (and tell me if this indicates a fundamental confusion): to get $q$, go to the $y$-value of the minimum (i.e. $aq^2$), take that value, divide by $a$, and then take the square root?"
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