1 - The equation is:
Since it has no variable on exponents and it has a term with x to the second power, this is a quadratic function.
2 - <em>x</em> represents the length of the tomato patch, so if we want the area of the bell pepper patch, we can input x = 8 into the function:
Thus, the area is 16 square feet.
3 - Since the leading coefficient is negative, the vertex of the parabola gives the maximum value for the function.
The <em>x</em> value of the vertex is:
So, in this case:
And to find the value for the area, we need to input that into the function:
Thus, the maximum area is 18 square feet.
4 - The value for the length of the tomato patch is just the corresponding <em>x</em> for this maximum, which we calculated as the vertex <em>x</em>:
Thus, the length of the tomato patch for this maximum value is 6 feet.