7. What is the range of the function f(x)=-x^2+60x 7 All real numbers that are greater than or equallo Dand less than or equal to 30 All real numbers that are greater than or equal to 0 and less than or equal to 60 All real numbers that are greater than or equal to 900 All real numbers that are less than or equal to 900

To find the range of the function $f(x)=-x^{2}+60x$, we need to determine the maximum and minimum values of the function.<br /><br />Step 1: Find the vertex of the parabola.<br />The vertex of a parabola in the form $f(x)=ax^2+bx+c$ is given by the formula $x=-\frac{b}{2a}$.<br />In this case, $a=-1$ and $b=60$, so the x-coordinate of the vertex is $x=-\frac{60}{2(-1)}=30$.<br /><br />Step 2: Find the y-coordinate of the vertex.<br />To find the y-coordinate of the vertex, we substitute the x-coordinate into the function:<br />$f(30)=-30^2+60(30)=-900+1800=900$.<br /><br />Step 3: Determine the range.<br />Since the parabola opens downwards (because the coefficient of $x^2$ is negative), the maximum value of the function occurs at the vertex. Therefore, the range of the function is all real numbers less than or equal to 900.<br /><br />Answer: All real numbers that are less than or equal to 900.