Vertex Form and Quadratic Functions

The video tutorial explains how to convert a quadratic function from its general form to vertex form. It begins by introducing the quadratic function and its forms, then demonstrates how to find the axis of symmetry using formulas. The tutorial continues with calculating the vertex of the parabola and converting the function into vertex form. Finally, it verifies the conversion graphically to ensure accuracy.

What is the standard form of a quadratic function?

• f(x) = a(x - h)^2 + k

• f(x) = a(x - h)(x - k)

• f(x) = ax + b

• f(x) = ax^2 + bx + c

Which form of a quadratic function is used to easily identify the vertex?

• Linear form

• Factored form

• Vertex form

• Standard form

What is the formula for the axis of symmetry in a quadratic function?

• x = -a / 2b

• x = b / 2a

• x = a / 2b

• x = -b / 2a

In the quadratic function f(x) = 2x^2 - x + 3, what is the value of 'a'?

• 1

• 2

• -1

• 3

What is the x-coordinate of the vertex for the function f(x) = 2x^2 - x + 3?

• 0

• -1/4

• 1/4

• 1/2

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

• Substitute x into the original function

• Use the formula y = -b / 2a

• Set y to zero

• Use the formula y = ax^2 + bx + c

What is the y-coordinate of the vertex for the function f(x) = 2x^2 - x + 3?

• 1/8

• 2

• 23/8

• 3

What is the vertex form of the quadratic function f(x) = 2x^2 - x + 3?

• f(x) = 2(x - 1/4)^2 + 23/8

• f(x) = 2(x - 1/4)^2 - 23/8

• f(x) = 2(x + 1/4)^2 - 23/8

• f(x) = 2(x + 1/4)^2 + 23/8

Why is it important to verify the vertex form graphically?

• To confirm the vertex coordinates are correct

• To ensure the parabola is a straight line

• To find the roots of the function

• To check if the function is linear

What does the vertex form of a quadratic function help to identify easily?

• The vertex of the parabola

• The y-intercept

• The roots of the function

• The slope of the line