Quadratic Equations: Standard to Vertex Form

This video tutorial explains how to convert quadratic equations from standard form to vertex form using two methods: completing the square and the vertex formula. It provides step-by-step instructions and examples for both methods, demonstrating how to find the vertex and rewrite the equation. The tutorial covers simple and complex quadratic equations, ensuring a comprehensive understanding of the conversion process.

What is the standard form of a quadratic equation?

• y = ax^2 + bx + c

• y = a(x - h)^2 + k

• y = ax + b

• y = ax^2 + bx

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

• The roots of the equation

• The coordinates of the vertex

• The coefficients of x and x^2

• The x-intercept and y-intercept

What is the first step in the completing the square method?

• Subtract the constant term

• Write the first two terms and take half of the coefficient of x

• Factor the quadratic equation

• Find the vertex coordinates

How do you find the x-coordinate of the vertex using the direct calculation method?

• By completing the square

• By factoring the equation

• By using the formula -b/2a

• By solving the equation ax^2 + bx + c = 0

What is the value of 'a' in the vertex form if the original equation is y = 2x^2 + 8x - 5?

• 8

• 2

• 5

• 1

When converting y = 2x^2 + 8x - 5 to vertex form, what is the x-coordinate of the vertex?

• -2

• -4

• 2

• 4

In the equation y = 3x^2 + 5x - 7, what is the first step in the completing the square method?

• Add 7 to both sides

• Divide all terms by 3

• Take out the GCF from the first two terms

• Multiply by 3

What is the y-coordinate of the vertex for the equation y = 3x^2 + 5x - 7 using the direct method?

• 25/12

• 19/12

• -25/12

• -19/12

What is the vertex form of the equation y = 3x^2 + 5x - 7?

• y = 3(x - 5/6)^2 - 109/12

• y = 3(x + 5/6)^2 + 109/12

• y = 3(x - 5/6)^2 + 109/12

• y = 3(x + 5/6)^2 - 109/12

Which method can be used to convert a quadratic equation from standard form to vertex form?

• Completing the square

• Direct vertex calculation

• Both methods

• Neither method