College Math CLEP Prep Practice Exam

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The graph of y = x^2 + 2x can be translated 6 units to the right and 3 units down. What is the equation of the translated graph?

y=x^2-4x-3
y=x^2-4x+3
y=x^2+4x-3
y=x^2+4x+3

The correct answer is: y=x^2+4x+3

When translating a function horizontally, the equation remains the same. The number being added or subtracted to x is the value of the horizontal shift. In this case, the graph is shifted 6 units to the right, so the equation remains as y=x^2+2x and we add 6 to the x values, making it y=x^2+(2+6)x. Simplifying this gives us y=x^2+8x. Similarly, when translating vertically, the number being added or subtracted is the value of the vertical shift. In this case, the graph is shifted 3 units down, so we subtract 3 from the function, making it y=x^2+8x-3. This is equivalent to option D, y=x^2+4x+3. The incorrect options have either a different constant or a different value being