Converting Quadratic Equations from Standard to Vertex Form

The video tutorial explains how to convert quadratic equations from standard form to vertex form. It highlights the similarities and differences between the two forms, focusing on the 'a' value and the vertex components 'H' and 'K'. The tutorial uses Desmos to graph equations and identify vertices, providing step-by-step examples to demonstrate the conversion process. Special cases, such as when the vertex is zero, are also discussed. The video emphasizes checking the conversion by graphing both forms to ensure they match.

What is one similarity between standard form and vertex form of a quadratic equation?

• Both have the same 'a' value.

• Both have the same 'k' value.

• Both have the same 'c' value.

• Both have the same 'h' value.

In standard form, what does the 'c' value represent?

• The axis of symmetry

• The x-intercept

• The y-intercept

• The vertex

What tool is used in the video to help find the vertex of a quadratic equation?

• Graphing calculator

• GeoGebra

• WolframAlpha

• Desmos

When converting from standard form to vertex form, what do you do with the x-value of the vertex?

• Keep it the same

• Add 'c' to it

• Change its sign

• Multiply it by 'a'

In the first example, what is the vertex of the equation y = x^2 + 6x + 11?

• (-2, 3)

• (3, -2)

• (-3, 2)

• (2, -3)

How can you verify that you have correctly converted an equation to vertex form?

• By comparing the graphs of both forms

• By checking the y-intercept

• By solving for x

• By finding the axis of symmetry

In the second example, what is the vertex of the equation y = -5x^2 + 8?

• (8, 0)

• (8, -5)

• (-5, 8)

• (0, 8)

Why is the vertex form of y = -5x^2 + 8 the same as its standard form?

• Because the 'c' value is zero

• Because the 'h' value is zero

• Because the 'a' value is negative

• Because the 'k' value is positive

In the third example, what is the vertex of the equation y = 2x^2 - 8x + 1?

• (4, -7)

• (2, -7)

• (-4, 15)

• (4, -15)

What happens if you forget to include the 'a' value when converting to vertex form?

• The y-intercept will be incorrect

• The graph will be too wide

• The vertex will be incorrect

• The graph will be too narrow