Exploring Vertical Translations of Quadratic Equations

This lesson covers vertical translations of quadratic functions, focusing on the parent function F(x) = x^2. It explains how transformations affect the graph's shape and position, comparing standard and vertex forms. Examples illustrate vertical translations, showing how changes in the K value shift graphs up or down. The lesson concludes by simplifying the process of identifying vertical translations in quadratic equations.

What is the basic quadratic function that serves as the parent function for all quadratic transformations?

• F(x) = x^2

• F(x) = x + 2

• F(x) = x^3

• F(x) = 2x

In the vertex form of a quadratic equation, what does the 'K' value represent?

• The slope of the graph

• The horizontal shift

• The axis of symmetry

• The vertical shift

In the context of quadratic functions, what does the term 'axis of symmetry' refer to?

• The line that represents the x-axis

• The lowest point on the graph

• The highest point on the graph

• The line that divides the parabola into two equal halves

When converting a quadratic equation from standard form to vertex form, what remains unchanged?

• The x-intercept

• The y-intercept

• The shape of the graph

• The coefficients of x

How does a vertical translation affect the graph of a quadratic function?

• It changes the width of the parabola

• It shifts the graph left or right

• It changes the direction of the parabola

• It shifts the graph up or down

If a quadratic function is written as G(x) = x^2 + 4, what type of transformation has occurred?

• Reflection over the x-axis

• Vertical translation downwards

• Vertical translation upwards

• Horizontal translation

What is the effect of a negative 'K' value in the vertex form of a quadratic equation?

• The graph shifts upwards

• The graph shifts downwards

• The graph becomes narrower

• The graph becomes wider