Transform the given quadratic function into vertex form f(x) = quadratic function into vertex form f(x) = quadratic function into vertex form by completing the square. by completing the square.

Vertex form:

The vertex is

Step-by-step explanation:

For a general quadratic function the form is:

For the function

The values of the coefficients for the function are the following: , ,

Take the value of b and divide it by 2. Then, the result obtained squares it.

Add and subtract

Write the expression of the form

The vertex is

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is