Aparabolic arch needs to be 5m high and 2m wide at ground level. find the quadratic equation which describes the arch.

Step-by-step explanation:

Given height of parabola is .

And wide at ground level.

Also, the parabola opens down.

Let us assume the parabola is aligned on Y-axis

As the height of parabola is . The maximum height of parabola is achieved when .

So, the vertex of parabola is .

The equation of parabola having vertex is.

.

Plugging the vertex of parabola

.

It is given that parabola is wide at the ground.

As the parabola is aligned on Y-axis. So, distance between X-intercept is .

The X-intercept would be

Plugging in the equation

Now, we get and having vertex .

So, the equation of parabola is

.

2^y = ln 5, or   y(ln 2) = ln 5.   solving for y,   y = (ln 5) / (ln 2).   y=5

step-by-step explanation:

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: