Chapter 1, Problem 1VE

Solution

To describe: how to determine whether a quadratic function in standard form has maximum or minimum value.

The only error is the outline of the parabola is a solid line not a dashed line.

A quadratic function of the form $y=a{x}^2+bx+c$ has vertex at $\left(-\frac{b}{2a},y\left(\frac{b}{2a}\right)\right)$ .

If $a>0$ then parabola is open upwards

If $a<0$ then parabola is open downwards.

A quadratic function in standard form has maximum value if $a<0$ .

The maximum value is $y\left(\frac{b}{2a}\right)$ .

A quadratic function in standard form has minimum value if $a>0$ .

The minimum value is $y\left(\frac{b}{2a}\right)$ .