Question

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Two open, downward facing parabolas of different sizes that share a vertex are plotted on a coordinate plane. 1 is a solid line and 1 is a dotted line.
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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)

Answer 1

3

Explanation: y = -3x^2 = 3·(-x^2), so every y-value of y = -x^2 is multiplied by 3 (a vertical stretch by factor 3).