Vertex Form and Quadratic Functions

This video tutorial teaches how to convert quadratic equations from standard form to vertex form by completing the square. It covers two examples: one where the leading coefficient (a) is 1 and another where a is not 1. The process involves moving the constant term, factoring out the leading coefficient, completing the square, and simplifying to find the vertex form. The video also explains how the vertex form reveals the vertex of the parabola and how transformations affect the graph.

What is the first step in converting a quadratic equation to vertex form?

• Multiply the equation by the leading coefficient

• Add the constant to both sides

• Subtract the constant from both sides

• Divide the equation by the leading coefficient

In the equation y = x^2 - 14x + 1, what is the value of B?

• 0

• 14

• -14

• 1

What is the vertex of the equation y = (x - 7)^2 - 48?

• (-7, 48)

• (7, 48)

• (-7, -48)

• (7, -48)

When the leading coefficient is not 1, what should you factor out?

• The leading coefficient

• The greatest common factor

• The B value

• The constant term

In the equation f(x) = 5x^2 - 40x + 7, what is the value of B?

• 40

• -40

• 5

• 7

What is the effect of the leading coefficient on the graph of a quadratic equation?

• It stretches or compresses the graph

• It shifts the graph up or down

• It shifts the graph left or right

• It reflects the graph over the x-axis

What is the vertex of the equation y = 5(x - 4)^2 - 73?

• (-4, -73)

• (4, 73)

• (-4, 73)

• (4, -73)

What is the purpose of completing the square in a quadratic equation?

• To find the y-intercepts

• To convert the equation to vertex form

• To convert the equation to standard form

• To find the x-intercepts

How do you determine the value to add when completing the square?

• Square the constant term

• Square the entire equation

• Square the leading coefficient

• Square half of the B value

What happens to the graph of a quadratic equation when the vertex form is used?

• It becomes a straight line

• It shifts according to the vertex

• It becomes a circle

• It remains unchanged