Converting Quadratic Functions: Standard to Vertex Form

This video tutorial by Mario from Mario's Math Tutoring explains how to convert quadratic equations from standard form to vertex form by completing the square. The lesson includes three examples: a simple quadratic with a leading coefficient of 1, a more challenging quadratic with an integer leading coefficient, and a complex quadratic with a negative fractional leading coefficient. Mario provides step-by-step instructions and tips to help students understand the process and apply it to different types of quadratic equations.

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

• Divide both sides by the leading coefficient

• Multiply both sides by the leading coefficient

• Add the constant term to both sides

• Subtract the constant term from both sides

In the first example, what value is added to both sides to complete the square?

• 8

• 6

• 17

• 9

What is the vertex of the quadratic equation y = (x + 3)^2 - 17?

• (3, 17)

• (-3, -17)

• (3, -17)

• (-3, 17)

In the second example, what is the leading coefficient of the quadratic equation?

• 1

• 2

• -2

• -1

When completing the square in the second example, what value is added inside the parentheses?

• 8

• 4

• 16

• 2

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

• (2, -7)

• (-2, 7)

• (2, 7)

• (-2, -7)

What is the tutor's main goal for his channel?

• To provide advanced math tutorials

• To make learning math more stressful

• To help students pass their exams

• To make learning math less stressful

In the third example, what is the leading coefficient of the quadratic equation?

• 1

• -1/2

• 2

• -2

What value is added to both sides when completing the square in the third example?

• -16

• 16

• -8

• 8

What is the vertex of the quadratic equation y = -1/2(x + 4)^2 + 11?

• (4, -11)

• (-4, 11)

• (-4, -11)

• (4, 11)