Question

The x-axis ranges from negative 5 to 5 in increments of 5. The y axis ranges from negative 15 to 5 in increments of 5. The dotted line parabola is plotted inside the solid line parabola. The solid line parabola is labeled y equals negative x squared. The solid parabola passes through the coordinates: left parenthesis negative 4 comma negative 15 right parenthesis, left parenthesis negative 3 comma negative 9 right parenthesis, left parenthesis negative 2 comma negative 4 right parenthesis, to the vertex at left parenthesis 0 comma 0 right parenthesis. The solid parabola continues through left parenthesis 2 comma negative 4 right parenthesis, left parenthesis 3 comma negative 9 right parenthesis, and left parenthesis 4 comma negative 15 right parenthesis. The dotted line parabola is labeled y equals negative 3 x squared. The dotted parabola passes through left parenthesis negative 2.2 comma negative 15 right parenthesis, left parenthesis negative 2 comma negative 12 right parenthesis, left parenthesis negative 1 comma negative 3 right parenthesis to the vertex at left parenthesis 0 comma 0 right parenthesis. The dotted parabola continues through left parenthesis 1 comma negative 3 right parenthesis, left parenthesis 2 comma negative 12 right parenthesis, and left parenthesis 2.2 comma negative 15 right parenthesis. All values are approximate.

Identify the k-value for the vertical stretch from the original function (the solid parabola) to the dilated function (the dotted parabola).

(1 point)
k=

Answer 1

k = 3

Explanation: y = -x^2 is multiplied by 3 to get y = -3x^2, and e.g. at x = 1: -1 → -3 (a factor of 3).