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.

Step-by-step explanation:

The Vertex form of a quadratic function is , where is the vertex of the parabola, and the sign of the coefficient indicates if the parabola opens down or opens up.

The Standard form of a quadratic function is , where the sign of the coefficient indicates if the parabola opens down or opens up.

To transform a quadratic function from Standard form  to Vertex form, you need to complete the square.

Given the quadratic function :

Indentify a:

Factor out -4:

Take the coefficient b and add and subtract to keep the balance:

Now rewrite the expression in the form , this is:

a) y = -3x +2

b) y = 1/2x -6

these 2 can be combined into one equation.

-3x +2 = .5x -6

8 = 3.5x

x = 8 / 3.5 = 2.2857142857

y = -3 * (8 / 3.5) +2

y = (-24 / 3.5) + 2

y = -4.8571428571

step-by-step explanation: