Guided Practice Write the equation of the parabola in vertex form. The vertex is (−4, −3) and the parabola passes through the point (−1, −48). Create a rough sketch of the graph to use as a visual aid.

A.
y = −16(x + 3)^2 + 4

B.
y = −5(x + 4)^2 − 3

C.
y = −(x − 4)^2 − 3

D.
y = −5(x − 4)^2 − 3

B.

y = −5(x + 4)^2 − 3

Step-by-step explanation:

Use the vertex and another point on the parabola to find the value of a. Then substitute the vertex (−4, −3) and a into the vertex form, y = a(x − h)2 + k.

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: