Question

PLZ HELP WILL GIVE 50 POINTS - QUADRATIC APPLICATIONS

Answer 1

Answer:

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

Step-by-step 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

$x_{v} = -\frac{b}{2a}$

$y_{v} = -\frac{\Delta}{4a}$

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

$x_{v} = -\frac{b}{2a} = -\frac{2.29}{2(-0.114)} = 10.04$

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