Standard form to vertex form of a quadratic

The video tutorial guides students through solving three quadratic problems using different methods. The instructor explains how to convert equations to standard form, find vertices, axes of symmetry, and intercepts. The first problem involves factoring and completing the square, the second problem focuses on completing the square, and the third problem demonstrates handling equations with no real roots. The tutorial emphasizes understanding the process and provides a step-by-step approach to each problem.

What steps should you follow to put the equation FX = 6X - X^2 into standard form?

Explain the process of factoring out a negative one when the leading coefficient is negative.

How do you find the vertex of the function after completing the square?

What is the significance of the axis of symmetry in a quadratic function?

Describe how to find the zeros of the function F(X) = 6X - X^2.

What is the process for completing the square for the equation H(X) = X^2 - 8X + 12?

How do you determine if a quadratic equation has real roots or not?