Question

Perez throws a stone on the pond. The path traveled by the stone can be modeled by y = -2x2 + 8x + 5, where x represents the time (in seconds) and y represents the height of the stone (in feet). What is the maximum height that the stone reaches

Answer 1

Answer:

The maximum height that the stone reaches is of 26 feet.

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 $y_{v}$.

y = -2x2 + 8x + 5

Quadratic function with $a = -2, b = 8, c = 5$

What is the maximum height that the stone reaches?

y value of the vertex. So

$\Delta = 8^2-4(-2)(5) = 64 + 40 = 104$

$y_{v} = -\frac{104}{4(-2)} = 26$

The maximum height that the stone reaches is of 26 feet.