Function Shifts and Vertex Analysis

The video tutorial explains how to use function shift rules to graph quadratic functions. It covers three examples: y = 2(x-4)^2 - 1, y = -(x+3)^2 + 2, and y = -4(x-4)^2 + 8. Each example demonstrates how to shift the graph horizontally and vertically, as well as how to apply vertical stretching and reflection. The tutorial provides step-by-step instructions for identifying the vertex and plotting key points to accurately graph each function.

What is the primary focus of this video tutorial?

• Graphing linear functions

• Using function shift rules to graph quadratic functions

• Solving quadratic equations

• Understanding polynomial functions

How does replacing x with (x-4) in the function y=2x^2 affect the graph?

• Shifts the graph down by 4 units

• Shifts the graph up by 4 units

• Shifts the graph left by 4 units

• Shifts the graph right by 4 units

What is the effect of subtracting 1 from the function y=2x^2?

• Shifts the graph up by 1 unit

• Shifts the graph down by 1 unit

• Shifts the graph right by 1 unit

• Shifts the graph left by 1 unit

What is the new vertex of the function y = 2(x-4)^2 - 1 after shifting?

• (0,-1)

• (4,-1)

• (4,0)

• (0,0)

What is the effect of a vertical stretch by a factor of 2 on y = 2x^2?

• The graph shifts down

• The graph becomes narrower

• The graph becomes wider

• The graph shifts up

What transformation does the negative sign in front of (x+3)^2 indicate?

• Vertical stretch

• Horizontal shift

• Reflection across the x-axis

• Reflection across the y-axis

How does replacing x with (x+3) affect the graph of y = -(x+3)^2 + 2?

• Shifts the graph right by 3 units

• Shifts the graph left by 3 units

• Shifts the graph up by 3 units

• Shifts the graph down by 3 units

What is the new vertex of the function y = -(x+3)^2 + 2 after shifting?

• (3,-2)

• (3,2)

• (-3,2)

• (-3,-2)

What is the shape of the graph of y = -x^2?

• A vertical line

• An upside-down parabola

• A horizontal line

• A right-side-up parabola

What happens to the graph of y = -x^2 when it is shifted left by 3 units?

• The vertex moves to (0,-3)

• The vertex moves to (0,3)

• The vertex moves to (-3,0)

• The vertex moves to (3,0)