A.7C Quadratic Transformation

A student graphs f(x) = -2x² + 4 on the coordinate grid. The student will change the coefficient of x² from -2 to another negative number to create g(x). How will the graph of g(x) compare with the graph of f(x)?

• The x-intercepts of g(x) and f(x) will be the same.

• g(x) will open in the opposite direction as f(x).

• The vertex of g(x) will be different from the vertex of f(x).

• g(x) will be wider or narrower than f(x).

• A

• B

• C

• D

• 2

• 8

• 14

• 20

• n = -19

• n = -1

• n = 1

• n = 19

• A

• B

• C

• D

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

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

• The y-intercept of the graph of h is 2 units below the y-intercept of the graph of g.

• The vertex of the graph of h is 2 units above the vertex of the graph of g.

If the vertex of the graph of a is 7 units below the vertex of the graph of b, which pair of functions could have been used to create the graphs of a and b?

Quadratic functions f and g are graphed on the same coordinate grid. If the vertex of the graph of f is 10 units above the vertex of the graph of g, which pair of functions could have been used to create the graphs of f and g?

• A reflection over the x-axis with a horizontal stretch

• A reflection over the y-axis with a horizontal stretch

• A reflection over the x-axis with a vertical stretch

• A reflection over the y-axis with a vertical stretch

• A reflection over the x-axis with a horizontal stretch

• A reflection over the y-axis with a horizontal stretch

• A reflection over the x-axis with a vertical stretch

• A reflection over the y-axis with a vertical stretch