Question

Determine the range of the function.

Answer 1

Answer:

$Solution: f(x)\ge-5\\Interval:[-5,\infty)$

Step-by-step explanation:

Equation: $\frac{1}{4} x^2-5 = y$

1). $\frac{1}{4} x^2-5 = y$ →$\frac{x^2}{4}-5=y$

2). $\frac{x^2}{4}-5=y$ ∴ $a=\frac{1}{4}, b=0, c=-5$

3). $x_v=-\frac{b}{2a}$

         $=-\frac{0}{2(\frac{1}{4})}$

         $=0$

4). now plug $x_v$ into $y_v$

$y_v=\frac{0^2}{4}-5$

    $=-5$

5). Minimum (0,-5) ∴ $f(x)\ge-5$