Question

Please help, I have to do this online so I’m getting stuckFunction p is a blank function. When the length of the tomato patch is 8ft, the area of the bell pepper patch is blank square feet. The maximum possible area of the bell pepper patch is blank square ft when the length of the tomato patch is blank ft

Answer 1

Function p is a quadratic function.

When the length of the tomato patch is 8ft, the area of the bell pepper patch is 16 square feet.

The maximum possible area of the bell pepper patch is 18 ft² when the length of the tomato patch is 6 ft

1) Gathering the data

P=-0.5x²+6x

2) Function p is a quadratic function.

This a quadratic function, whose coefficient a is negative (-0.5) and its graph is a parabola

3) When the length of the tomato patch is 8ft, the area of the bell pepper patch is 16 square feet.

Since p is the area of the bell pepper patch

x for the length of the tomato patch

P(8)= -0.5(8)²+6(8)

P(8)=-0.5(64)+48

P(8)=-32+48

P(8)=16 ft²

4) The maximum possible area of the bell pepper patch is 18 square ft when the length of the tomato patch is 6 ft

The maximum possible area is found by

`\begin{gathered} X_v,Y_v\text{ = (}(-b)/(2a),(-\Delta)/(4a)) \\ ((-6)/(2(-0.5)),-(36-4(-0.5)(0))/(4(-0.5))) \\ ((-6)/(-1),-(36)/(-2)) \\ (6,\text{ 18)} \end{gathered}`

So