y=-(x+6)(x-4) Find the domain and range of the function. Domain All real numbers

## Step 1The given function is a quadratic function, which indicates that y will be any real number depending on x. Thus, since x can indeed be any real number, we can find an x-value that fits into the range.## Step 2For quadratic functions, the shape of the graph is a parabola. If the coefficient of is positive, the parabola shifts upward; if it’s negative, the parabola shifts downward. Here the coefficient of (`-1`) is negative, the shape of the quadratic function is an inverted curve, which tells us that it will have a maximum value and then go to negative infinity.## Step 3Hence, for the range, since y can take any value below this maximum, the range will also be the set of all real numbers equal to or below this particular maximum point. The highest point (or y-coordinate of the vertex of the downside parabola) of this function is determined by finding the value of y using the x-coordinate of the vertex of the parabola given by the formula `(-b/2a)`## Step 4So first we find the 'x' which is the axis of symmetry or the x-value of the vertex by using formula -b/(2a). The standard quadratic equation is where### **a = -1, b = -2**## Step 5Hence, the 'x' will be `-(-2)/2*(-1) = 1`. ## Step 6Putting this x = 1 into the equation will result y = 27 which is the maximum value, as this is an inverted parabola.## Step 7Hence, the range is the set of all real numbers equal to or less than y = `27`.