How do I find the domain and range of 2x^2-7?

Question

anonymous · Answer

Hey there.
That equation bases from the original formula of $$y=ax ^{2}+bx+c$$., where a is the value attached to the x^2 variable, b is the value attached to the x variable and c is attached to no variable.
Often, the domain of a parabola is $$x$$, which also applies to this one. To find y-vertex, which is the tip of the parabola is by using the formula$$y _{v}=\frac{ b ^{2}-4ac }{ 4a }$$. After this, we replace the values, being$$y _{v}=\frac{ 0^{2}-4*2*(-7) }{ 4*2 }=7$$.
It is also important to take account of the a value. When it is positive, the parabola is U-shaped and when it is negative, it is cap-shaped.
In this case the a is positive, giving us the clue that the vertex is at the bottom, with y-value equivalent to 7. It then goes up to infinity. Hence, the range is $$y \ge7$$

anonymous · Answer

The parabola of the graph is $$x \in \mathbb{R} $$

anonymous · Answer

That is the domain.