Vertex Form and Quadratic Functions

The video tutorial explains how to convert a quadratic function from standard form to vertex form. It begins by identifying the coefficients of the quadratic equation and then calculates the axis of symmetry. The tutorial proceeds to find the vertex coordinates and uses them to rewrite the function in vertex form. Finally, the video verifies the conversion by graphing the equations to ensure they represent the same parabola.

What is the standard form of a quadratic function?

• f(x) = a(x - h)^2 + k

• f(x) = ax + b

• f(x) = a(x + h)^2 - k

• f(x) = ax^2 + bx + c

What is the vertex form of a quadratic function?

• f(x) = ax^2 + bx + c

• f(x) = a(x - h)^2 + k

• f(x) = ax + b

• f(x) = a(x + h)^2 - k

How do you find the x-coordinate of the vertex?

• x = -b / 2a

• x = a / 2b

• x = b / 2a

• x = -b / a

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

• x = -b / a

• x = b / 2a

• x = a / 2b

• x = -b / 2a

If the x-coordinate of the vertex is -1, what is the y-coordinate when evaluated in the function f(x) = 3x^2 + 6x + 8?

• 9

• 3

• 5

• 7

What is the value of 'a' in the vertex form if the standard form is f(x) = 3x^2 + 6x + 8?

• 1

• 2

• 3

• 4

What is the vertex of the quadratic function f(x) = 3(x + 1)^2 + 5?

• (-1, 5)

• (1, -5)

• (1, 5)

• (-1, -5)

How do you verify the vertex form of a quadratic function graphically?

• By calculating the discriminant

• By checking the y-intercept

• By comparing the graphs of standard and vertex forms

• By finding the roots

What happens to the graph of a quadratic function when you change the value of 'a' in the vertex form?

• It reflects over the x-axis

• It shifts horizontally

• It shifts vertically

• It becomes wider or narrower

What is the effect of adding a positive constant to the vertex form of a quadratic function?

• The graph shifts right

• The graph shifts left

• The graph shifts down

• The graph shifts up