Question

Use the image to answer the question.

Two parabolas are graphed on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 5 to 5 in increments of 1.
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The first parabola is solid and passes through coordinates left parenthesis negative 2 comma negative 4 right parenthesis, left parenthesis negative 1 comma negative 1 right parenthesis, left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma negative 1 right parenthesis, and left parenthesis 2 comma negative 4 right parenthesis. The second parabola is dotted and passes through coordinates left parenthesis negative 1 comma negative 4 right parenthesis, left parenthesis 0 comma negative 3 right parenthesis, and left parenthesis 1 comma negative 4 right parenthesis.

The function graphed with a blue dotted line is translated to the function graphed as a solid orange line. If the same translation were applied to the solid orange function, what would be the coordinates of the new y-intercept (not pictured)?

Answer 1

The dotted graph is y = -x^2 - 3 and the solid graph is y = -x^2, so the dotted was translated up 3 to get the solid. Applying the same up-3 translation to the solid gives y = -x^2 + 3, whose y-intercept is (0, 3).