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Chapter 9: Q4. (page 597)

Considery=x2鈭�7x+6. State the maximum or minimum value.

Short Answer

Expert verified

The function y=x2鈭�7x+6 has a minimum value x=1.5.

Step by step solution

01

Step 1. Define the concept.

In a quadratic equation y=ax2+bx+c, if the coefficient of x2is positive, then the graph of the parabola is upward open and vertex is at the minimum and if the coefficient of x2is negative, then the graph of the parabola is downward open and vertex is at maximum.

The graph of any quadratic function is a parabola.

localid="1647858376445" y=ax2+bx+c(a is positive) 鈥� minimum

localid="1647858353989" y=ax2+bx+c(a is negative) 鈥� maximum

02

Step 2. Graphical representation of the quadratic function.

Draw the graph of the function: y=x2鈭�7x+6.

03

Step 3. State whether the function has a maximum or minimum value.

The function y=x2鈭�7x+6, the coefficient of x2is positive; it is upward open, so it has a minimum value x=1.5.

Thus, the function y=x2鈭�7x+6has a minimum value x=1.5.

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