Exploring Quadratic Transformations

The video tutorial introduces quadratic functions and their transformations, including horizontal and vertical translations, vertical stretching and shrinking, and reflections. It explains the vertex form of quadratic functions and demonstrates how to write equations based on described transformations. The tutorial provides a comprehensive review of these concepts, helping students understand and apply them to graphing and solving quadratic equations.

What is the standard form of a quadratic function?

• ax + b

• ax^2 + bx

• x^2 + bx + c

• ax^2 + bx + c

What does the 'c' represent in the standard form of a quadratic equation ax^2 + bx + c?

• The y-intercept

• The focus

• The x-intercept

• The vertex

Tags

CCSS.HSF-IF.C.7A

What does a horizontal shift to the right in the graph of a quadratic function indicate?

• Division inside the function

• Subtraction inside the function

• Addition inside the function

• Multiplication inside the function

Which transformation involves changing the y-values of a quadratic function?

• Horizontal stretch

• Horizontal shift

• Vertical stretch

• Reflection over the x-axis

What does a horizontal translation to the left in a quadratic function's graph typically involve?

• Dividing the x variable inside the function

• Subtracting from the x variable inside the function

• Multiplying the x variable inside the function

• Adding to the x variable inside the function

In the context of quadratic functions, what does a vertical translation downward imply?

• Division of the function outside the brackets

• Multiplication of the function outside the brackets

• Subtraction from the function outside the brackets

• Addition to the function outside the brackets

What effect does a vertical stretch by a factor of 2 have on the points of a quadratic function?

• Doubles the x-values of the points

• Halves the y-values of the points

• No change to the points

• Doubles the y-values of the points

What information can be directly obtained from the vertex form of a quadratic equation?

• The slope of the parabola

• The maximum value of the function

• The intercepts of the parabola

• The vertex of the parabola

What is indicated by a negative 'a' value in the vertex form of a quadratic equation?

• The parabola is narrower than usual

• The parabola is wider than usual

• The parabola opens downwards

• The parabola opens upwards

Tags

CCSS.HSF-IF.C.7A

How is a quadratic function affected by a reflection over the y-axis?

• It shifts to the right

• It flips over the y-axis

• It shifts to the left

• It becomes narrower