Writing Quadratic Equations in Vertex Form

This lesson teaches how to find the maximum or minimum value of a quadratic function by converting it to vertex form. It explains the properties of quadratic functions, such as their graph being a parabola, and how the sign of the leading coefficient affects the function's maximum or minimum value. The lesson covers completing the square, common errors, and applies these concepts to a real-world problem involving a baseball's trajectory. By finding the vertex, students can determine the maximum height and time to reach it. The lesson concludes with a summary of key points.

What determines whether a quadratic function has a maximum or minimum value?

• The x-coordinate of the vertex

• The value of the coefficient 'c'

• The value of the coefficient 'b'

• The sign of the coefficient 'a'

What is a common mistake when completing the square with a negative coefficient?

• Ignoring the linear term

• Forgetting to add the constant term

• Incorrectly factoring out the negative coefficient

• Multiplying the quadratic term by zero

In the baseball problem, what is the initial height of the ball?

• 10 feet

• 5 feet

• 0 feet

• 64 feet

How long does it take for the baseball to reach its maximum height?

• 4 seconds

• 3 seconds

• 2 seconds

• 1 second

What is the maximum height reached by the baseball?

• 64 feet

• 53 feet

• 69 feet

• 75 feet