We want to find the range of the given quadratic function.
y=- 4x^2-1/2
To do so, we will graph it and make a table of values first.
x
- 4x^2-1/2
y=- 4x^2-1/2
0
- 4( 0)^2-1/2
- 1/2
1
- 4( 1)^2-1/2
- 41/2
2
- 4( 2)^2-1/2
- 161/2
Note that since the given function has the form y=ax^2+c the axis of symmetry is the vertical line x= 0. Now, let's plot the obtained points and their reflections across the axis of symmetry. Then we can connect them with a parabola.
We can see above that the x-variable can take any value.
Conversely, the y-variable only takes values less than or equal to - 12. Using this information, we can write the domain and range of the function.
Domain:& {All real numbers}
Range:& {y | y≤ - 12}
