Vertex Form and Quadratic Functions

The video tutorial explains how to identify the vertex of a quadratic function by understanding its translation from the origin. It reviews basic concepts of vertical and horizontal translations, introduces the vertex form of a quadratic equation, and demonstrates how to complete the square. Examples are provided to illustrate these concepts, and common mistakes are discussed to help learners avoid them.

What is the vertex of the function f(x) = x^2?

• (0, 0)

• (3, 3)

• (1, 1)

• (2, 2)

How does adding a constant k to a function affect its graph?

• It compresses the graph horizontally.

• It stretches the graph vertically.

• It shifts the graph vertically by k units.

• It shifts the graph horizontally by k units.

What is the effect of subtracting a value h inside the parentheses of a quadratic function?

• It results in a horizontal compression.

• It results in a horizontal translation by h units.

• It results in a vertical translation by h units.

• It results in a vertical stretch.

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^2 + k

• f(x) = a(x + h)^2 + k

What process is used to rewrite a quadratic function in vertex form?

• Graphing

• Using the quadratic formula

• Completing the square

• Factoring

In the function f(x) = (x - 3)^2 + 4, what is the vertex?

• (3, 4)

• (-3, 4)

• (-3, -4)

• (3, -4)

If a function is translated horizontally by -2 units and vertically by -3 units, where is the new vertex?

• (-2, 3)

• (-2, -3)

• (2, -3)

• (2, 3)

What is a common mistake when identifying the vertex from the vertex form?

• Forgetting to complete the square

• Using the same sign for h inside the parentheses

• Ignoring the constant k

• Using the opposite sign for k

In the vertex form f(x) = (x + 4)^2 + 3, what is the correct vertex?

• (-4, 3)

• (4, 3)

• (4, -3)

• (-4, -3)

Why is it important to take the opposite of the constant term inside the parentheses when identifying the vertex?

• To determine the direction of the parabola

• To find the axis of symmetry

• To ensure the correct horizontal translation

• To ensure the correct vertical translation