Linear and Quadratic Transformations

Quadratic functions p and q are graphed on the grid. The graph of p was transformed to create the graph of q. Which function best represents the graph of q?

• The graph of g is a reflection of the graph of f across the x-axis.

• The vertex of the graph of g is 9 units to the right of the vertex of the graph of f.

• The graph of g is reflection of the graph of f across the y-axis.

• The y-intercept of the graph of g is 9 units below the y-intercept of the graph of f.

Mathematical Equivalence

ON

• translate six right and 7 up

• translate six left and 7 up

• translate six right and 7 down

• translate six left and 7 down

Given f(x) = ax² , if 0 < a < 1 , the graph will transform by

• becoming wider or vertically compressed

• becoming narrower or vertically stretched

Given f(x) = (x + 6)² - 2 , how did we transform from the parent function?

• Horizontal shift left 6, vertical shift up 2

• Horizontal shift left 6, vertical shift down 2

• Horizontal shift right 6, vertical shift down 2

• Horizontal shift right 6, vertical shift up 2

What is the vertex of this equation?

• (4, 6)

• (-4, -6)

• (-4, 6)

• (4, -6)

• vertical shrink factor 1/4, reflect over y-axis, translate down 1

• vertical stretch factor 1/4, reflect over x-axis, translate down 1

• vertical shrink factor 1/4, reflect over x-axis, translate down 1

• horizontal shrink factor 4, reflect over y-axis, translate down 1

What is the vertex form of a quadratic function?

• f(x) = 2a(x - h)² + k

• f(x) = a(x - h)² + k

• f(x) = (x + h)² + k

• f(x) = a(x - h) - k

In the vertex form f(x) = a(x - h)² + k , what does the 'a' value do?

• Shifts the function left or right

• Changing 'a' value has no affect on the parent function

• Vertical stretch or compression

• Shifts the function up or down