Chapter 8.8, Problem 17OE

To determine

To find: Whether the graph of the given quadratic function has minimum or maximum point.

Answer to Problem 17OE

The graph of the given quadratic function has minimum point.

Explanation of Solution

Given information:

The given function is,

  $T:x\to 8x^2+x-6$

Concept used:

For the quadratic equation, if the leading coefficient that is coefficient of $x^2$ is greater than zero then the graph opens in upward direction or if less than zero than opens in downward direction.

If the graph opens in upward direction, then it has minimum point and if open in downward direction then it has maximum point.

The given function is,

  $T:x\to 8x^2+x-6$

The leading coefficient of the equation is $8>0$ .

For the quadratic equation, if the leading coefficient that is coefficient of $x^2$ is greater than zero then the graph opens in upward direction or if less than zero than opens in downward direction.

If the graph opens in upward direction, then it has minimum point and if open in downward direction then it has maximum point.

Hence, the graph of the given quadratic function has minimum point.