Question

The graph shows the function representing the recommended amount of mulch, in cubic yards, for circular flowerbeds based on the radius of the flowerbed in feet.



If the vertex of the function is at the point (0, 0.5), what is the recommended amount of mulch for a flowerbed with a radius of 20 feet? Round to the nearest tenth if necessary.

7 cubic yards
12.5 cubic yards
25.5 cubic yards
31 cubic yards

Answer 1

Answer: 12.5 cubic yards

Step-by-step explanation:

This answer is 100% correct for edge.nuity and e2020.

Answer 2

The recommended amount of mulch for a flowerbed with a radius of 20 feet is 12.5 cubic yards

An quadratic function is represented as:

• $y =ax^2 + bx + c$

The vertex (i.e. the minimum point) is given as

• $(x,y)=(0.0.5)$

So, we have:

$y =ax^2 + bx + c$

$0.5 =a(0)^2 + b(0) + c$

$0.5 = c$

Rewrite as:

$c =0.5$

So, we have:

$y =ax^2 + bx + 0.5$

On the graph, we have:

$(x,y) = (4,1)$

So, we have:

$1 =a(4)^2 + 4b + 0.5$

$1 =16a + 4b + 0.5$

The equation becomes

$16a + 4b = 0.5$

On the graph, we have:

$(x,y) = (11,4)$

So, we have:

$4 =a(11)^2 + 11b + 0.5$

$4 =121a + 11b + 0.5$

The equation becomes

$121a + 11b = 3.5$

So, we have:

$16a + 4b = 0.5$

$121a + 11b = 3.5$

Using a graphing calculator, we have:

$(a,b) = (0.0276,0.01461)$

So, the quadratic equation is:

$y = 0.0276x^2 + 0.01461x + 0.5$

When the radius is 20, the equation becomes

$y = 0.0276 \times 20^2 + 0.01461\times 20 + 0.5$

$y = 11.8$

The closest to 11.8 is 12.5.

Hence, the recommended amount of mulch for a flowerbed with a radius of 20 feet is 12.5 cubic yards

Read more about quadratic functions at:

https://brainly.com/question/11631534