Quadratic Functions and Vertex Form

The video tutorial explains how to convert a quadratic equation from its general form to the standard form by finding the vertex. It covers the calculation of vertex coordinates using the formula h = -b/2a and k = f(-b/2a), and demonstrates rewriting the equation in standard form. The tutorial also includes verification of the conversion through algebraic expansion and graphical representation, ensuring the accuracy of the transformation.

What is the general form of a quadratic equation?

• y = ax^3 + bx^2 + cx + d

• y = mx + b

• y = a(x - h)^2 + k

• y = ax^2 + bx + c

In the vertex form of a quadratic equation, what do the variables h and k represent?

• The vertex of the parabola

• The slope and y-intercept

• The coefficients of x and x^2

• The x-intercepts

How do you calculate the x-coordinate of the vertex in a quadratic equation?

• -c / b

• c / a

• -b / 2a

• b / 2a

What is the y-coordinate of the vertex for the equation y = 2x^2 - 12x + 5?

• 3

• 5

• 0

• -13

What is the standard form of the quadratic equation y = 2x^2 - 12x + 5?

• y = 2(x + 3)^2 + 13

• y = 2(x + 3)^2 - 13

• y = 2(x - 3)^2 + 13

• y = 2(x - 3)^2 - 13

Why is it more common to write minus 13 instead of plus negative 13 in the standard form?

• It simplifies the equation

• It is a mathematical convention

• It changes the equation

• It is easier to read

What is the result of expanding the expression (x - 3)^2?

• x^2 - 6x + 9

• x^2 + 6x + 9

• x^2 - 9

• x^2 + 9

How can you verify that the transformation to standard form is correct?

• By graphing the equations

• By comparing the y-intercepts

• By checking the coefficients

• By solving for x

What is the y-intercept of the quadratic equation y = 2x^2 - 12x + 5?

• 5

• 3

• -13

• 0

What does the graph of a quadratic function typically look like?

• A parabola

• A straight line

• An ellipse

• A circle