Respuesta :
Answer:
The highest point the football will reach is of 180.5 feet.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
In this question:
The height of the ball is given by the following equation:
[tex]f(x) = -0.02x^2 + 2.2x + 12[/tex]
Which is the highest point the football will reach, in feet?
This is the value of f at the vertex.
We have that: [tex]a = -0.02, b = 2.2, c = 12[/tex]
So
[tex]\Delta = (2.2)^2 -4(-0.2)(12) = 14.44[/tex]
[tex]y_{v} = -\frac{\Delta}{4a} = -\frac{14.44}{4(-0.02)} = 180.5[/tex]
The highest point the football will reach is of 180.5 feet.
