exercise:11b69f4519: Difference between revisions
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<li>Which of the constants <math>a</math>, <math>b</math>, and <math>c</math> determines | <li>Which of the constants <math>a</math>, <math>b</math>, and <math>c</math> determines | ||
the type of extreme point of the graph?</li> | the type of extreme point of the graph?</li> | ||
<li> | <li> | ||
What is the extreme value of | What is the extreme value of | ||
<math>ax^2 + bx + c</math>?</li> | <math>ax^2 + bx + c</math>?</li> | ||
<li>Write <math>ax^2 + bx + c</math> as <math>a \left( x^2 + \frac ba x \right) + c</math>, | <li>Write <math>ax^2 + bx + c</math> as <math>a \left( x^2 + \frac ba x \right) + c</math>, complete the square on <math>x^2 + \frac ba x</math> without changing the function, and find the result of (c) algebraically.</li> | ||
complete the square on <math>x^2 + \frac ba x</math> without changing | |||
the function, and find the result of | |||
</ul> | </ul> | ||
Latest revision as of 00:39, 23 November 2024
[math]
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[/math]
- Show that the graph of the function [math]ax^2 + bx + c, a \ne 0[/math], always has an absolute extreme point.
- Which of the constants [math]a[/math], [math]b[/math], and [math]c[/math] determines the type of extreme point of the graph?
- What is the extreme value of [math]ax^2 + bx + c[/math]?
- Write [math]ax^2 + bx + c[/math] as [math]a \left( x^2 + \frac ba x \right) + c[/math], complete the square on [math]x^2 + \frac ba x[/math] without changing the function, and find the result of (c) algebraically.