How to find the vertex of a parabola in vertex form

The video tutorial explains how to solve a quadratic equation by finding its vertex and X-intercepts. It begins with an introduction to the problem and the standard form of a quadratic equation. The instructor then demonstrates how to identify the vertex using the standard form and clarifies common misconceptions. Next, the process of finding X-intercepts is discussed, highlighting the issue of non-real roots in this particular problem. The tutorial concludes with a brief mention of imaginary roots, which will be covered in future lessons.

What is the standard form of a quadratic equation?

• F(x) = ax^2 + bx + c

• F(x) = (x - h)^2 + k

• F(x) = ax + b

• F(x) = a(x - h)(x - k)

In the quadratic function F(x) = (x - 6)^2 + 3, what are the coordinates of the vertex?

• (6, 3)

• (3, 6)

• (-6, 3)

• (6, -3)

Why is it incorrect to say the vertex of F(x) = (x - 6)^2 + 3 is (-6, 3)?

• Because the vertex is determined by the number outside the parenthesis

• Because the vertex is always positive

• Because the vertex is determined by the opposite sign of the number inside the parenthesis

• Because the vertex is always negative

What happens when you try to find the X-intercepts of F(x) = (x - 6)^2 + 3?

• You find no real roots

• You find one real root

• You find imaginary roots

• You find two real roots

Why can't you take the square root of a negative number when finding X-intercepts?

• Because it results in a complex number

• Because it results in zero

• Because it results in a positive number

• Because it results in a negative number