A person who is standing on a ledge throws a rock into the air. The rock reaches a maximum height of 676 feet above the ground after 1.5 seconds.

If the rock hits the ground below the ledge 8 seconds after it is thrown, which quadratic function can be used to find

the height of the rock above the ground t seconds after it is thrown?

The quadratic equation is

Step-by-step explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

It's vertex is the point

In which

Where

If a<0, the vertex is a maximum point, that is, the maximum value happens at , and it's value is .

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

.

This polynomial has roots such that , given by the following formulas:

Quadratic equation:

The rock reaches a maximum height of 676 feet above the ground after 1.5 seconds.

This means that:

If the rock hits the ground below the ledge 8 seconds after it is thrown

This means that:

Relation of b and a:

This means that:

Relationship of c and a:

Finding a:

Since it is a quadratic equation, a cannot be 0.

Finding b and c:

The quadratic equation is given by:

The quadratic equation is

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source:

hope it

step-by-step explanation:

x^(1/6) · x^(1/6) · x^(1/6)   ·x^(1/6) = x^(4/6)   since we add the exponents

4/6 can be simplified to 2/3

the simplified form is x^(2/3)