Question

Graph ​h(x)=−x^2+8​.

Answer 1

The dimensions that give the largest area for the rectangle are a width of
`(4 √(2))` and a height of 8.

The graph of the function (h(x) = -x^2 + 8) is a parabola that opens downward and has its vertex at the point (0, 8). The coefficient of the (x^2) term is negative, which means that the parabola opens downward.

The vertex of the parabola is the point where the parabola changes direction. In this case, the vertex is at the point (0, 8), which means that the parabola opens downward and its axis of symmetry is the y-axis.

The parabola intersects the x-axis at the points
`((√(8), 0))` and
`((- √(8), 0))`. Therefore, the width of the rectangle is
`(2 √(8) = 4 √(2))` and the height of the rectangle is 8.

Therefore, the dimensions that give the largest area for the rectangle are a width of
`(4 √(2))` and a height of 8.