Question

PLZ HELP WILL GIVE 50 POINTS - QUADRATIC APPLICATIONS

find how far away (ground distance) from the catapult will white bird be at its highest. (round to the nearest 2 decimal points)
h= -0.114x^2+2.29x+3.5

Answer 1

The bird will be at a ground distance of 10.04 units away.

Explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

`f(x) = ax^(2) + bx + c`

It's vertex is the point
`(x_(v), y_(v))`

In which

`x_(v) = -(b)/(2a)`

`y_(v) = -(\Delta)/(4a)`

Where

`\Delta = b^2-4ac`

If a<0, the vertex is a maximum point, that is, the maximum value happens at
`x_(v)`, and it's value is
`y_(v)`.

Equation for the height:

The height of the bird after x seconds is given by:

`h(x) = -0.114x^2 + 2.29x + 3.5`

Which is a quadratic equation with
`a = -0.114, b = 2.29, c = 3.5`.

When the bird is at its highest?

Quadratic equation with
`a < 0`, and thus, at the vertex. The ground distance is the x-value of the vertex. Thus

`x_(v) = -(b)/(2a) = -(2.29)/(2(-0.114)) = 10.04`

The bird will be at a ground distance of 10.04 units away.