Look carefully at the function rule.
f(x)=-2x^2+6We can see that given function is quadratic. Therefore, it belongs to the family of quadratic functions, with a parent function of y=x^2.
Domain
Unless specific restrictions are given, the domain of quadratic functions is usually all real numbers.
Domain:& - ∞ < x < ∞
Range
The range of quadratic functions depends on the y-coordinate of the vertex, so let's find this value first.
f(x)=-2x^2+6 ⇔ f(x)=-2x^2+ x+6
We can see above that a=-2, b= , and c=6. To calculate the vertex, we need to think of y as a function of x, as y=f(x). We can write the expression for the vertex by stating the x- and y-coordinates in terms of a and b.
Vertex: ( - b/2a, f( - b/2a ) )
By substituting - 2(-2)=0 for x in the function rule, we can solve for the y-coordinate.
Since the y-coordinate of vertex equals 6, and the parabola opens downwards (because a<0), the range of this function is all real numbers less than or equal to 6.
Range:& y ≤ 6
Checking the Answer
To verify your answer, enter the function rule in the calculator by pushing Y= and writing the function rule in the first row. Next, by pushing GRAPH, the calculator will draw the graph of the function.
Looking at the graph, we can confirm that our solution is correct.
