Vertex Form and Quadratic Functions

The video tutorial explains how to convert a quadratic function from general form to vertex form. It begins by introducing the general and vertex forms of quadratic functions. The tutorial then demonstrates how to find the vertex using formulas for the axis of symmetry and vertex coordinates. It proceeds to calculate the x and y coordinates of the vertex and shows how to write the function in vertex form. Finally, the video verifies the conversion by graphing the functions and concludes with a summary of the process.

What is the general form of a quadratic function?

• f(x) = ax^2 + bx + c

• f(x) = a(x - h)^2 + k

• f(x) = ax + b

• f(x) = ax^3 + bx^2 + cx + d

Which formula is used to find the x-coordinate of the vertex?

• x = -b / 2a

• x = b / 2a

• x = -a / 2b

• x = a / 2b

What are the values of a, b, and c in the quadratic function f(x) = x^2 - 4x + 5?

• a = -1, b = 4, c = 5

• a = 1, b = -4, c = 5

• a = 1, b = 4, c = -5

• a = 1, b = -4, c = -5

What is the x-coordinate of the vertex for the function f(x) = x^2 - 4x + 5?

• 2

• -2

• 4

• -4

How do you calculate the y-coordinate of the vertex once you have the x-coordinate?

• Add b to the x-coordinate

• Divide the x-coordinate by c

• Multiply the x-coordinate by a

• Substitute the x-coordinate into the original function

What is the vertex of the quadratic function f(x) = x^2 - 4x + 5?

• (-2, -1)

• (-2, 1)

• (2, -1)

• (2, 1)

What is the vertex form of the function f(x) = x^2 - 4x + 5?

• f(x) = (x - 2)^2 + 1

• f(x) = (x + 2)^2 - 1

• f(x) = (x - 2)^2 - 1

• f(x) = (x + 2)^2 + 1

Why can the coefficient 'a' be omitted in the vertex form if it equals 1?

• Because it is negative

• Because it is not needed in any form

• Because it is always zero

• Because multiplying by 1 does not change the value

What should you do to verify the correctness of the vertex form derived from a quadratic function?

• Calculate the derivative

• Solve for x-intercepts

• Check the discriminant

• Graph both forms and compare

What is the vertex of the parabola when graphed?

• (-2, -1)

• (1, 2)

• (-1, -2)

• (2, 1)