Question

Determine the range of the function.

y=1/4x^2 - 5



a.All real numbers.

b.All integers less than or equal to -5.

c.All integers greater than or equal to -5.

d.All real numbers greater than or equal to -5.

Answer 1

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

Explanation:

Equation:
`(1)/(4) x^2-5 = y`

1).
`(1)/(4) x^2-5 = y` →
`(x^2)/(4)-5=y`

2).
`(x^2)/(4)-5=y` ∴
`a=(1)/(4), b=0, c=-5`

3).
`x_v=-(b)/(2a)`

`=-(0)/(2((1)/(4)))`

`=0`

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

`y_v=(0^2)/(4)-5`

`=-5`

5). Minimum (0,-5) ∴
`f(x)\ge-5`