Vertex and Quadratic Functions Concepts

The video tutorial explains how to convert a quadratic function from standard form to vertex form. It begins by identifying the coefficients and using them to find the axis of symmetry and the vertex. The tutorial then demonstrates how to calculate the y-coordinate of the vertex and rewrite the function in vertex form. Finally, it verifies the conversion graphically by showing that both forms represent the same parabola.

What is the general form of a quadratic function?

• f(x) = ax^3 + bx^2 + cx + d

• f(x) = ax + b

• f(x) = a(x - h)^2 + k

• f(x) = ax^2 + bx + c

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

• x = b / 2a

• x = -a / 2b

• x = a / 2b

• x = -b / 2a

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

• Using the formula x = a / 2b

• Using the formula x = -a / 2b

• Using the formula x = -b / 2a

• Using the formula x = b / 2a

What is the next step after finding the x-coordinate of the vertex?

• Find the roots of the equation

• Convert to standard form

• Graph the function

• Calculate the y-coordinate using f(x)

How do you calculate the y-coordinate of the vertex?

• By evaluating f(a / 2b)

• By evaluating f(-a / 2b)

• By evaluating f(-b / 2a)

• By evaluating f(b / 2a)

What is the vertex form of a quadratic function?

• f(x) = a(x - h)^2 + k

• f(x) = ax^2 + bx + c

• f(x) = ax + b

• f(x) = ax^3 + bx^2 + cx + d

What remains the same when converting from standard form to vertex form?

• The value of 'c'

• The value of 'b'

• The value of 'a'

• The value of 'h'

What is the significance of the vertex in the graph of a quadratic function?

• It is the midpoint of the graph

• It is the point where the graph intersects the y-axis

• It is the point where the graph intersects the x-axis

• It is the highest or lowest point on the graph

How can you verify the vertex form of a quadratic function?

• By graphing and checking the vertex

• By calculating the discriminant

• By solving for x-intercepts

• By finding the derivative

What does the graph of a quadratic function look like?

• An ellipse

• A parabola

• A straight line

• A circle