The function m is given in three equivalent forms. Which form most quickly reveals the y-intercept? Choose 1 answer: (A) m(x)=2x^(2)+16 x+24 (B) m(x)=2(x+4)^(2)-8 (C) m(x)=2(x+6)(x+2) What is the y-intercept? y-intercept =(0,◻)

Question

The function  m is given in three equivalent forms. Which form most quickly reveals the  y-intercept? Choose 1 answer: (A)  m(x)=2x^(2)+16 x+24 (B)  m(x)=2(x+4)^(2)-8 (C)  m(x)=2(x+6)(x+2) What is the  y-intercept?  y-intercept  =(0,◻)

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Definition: The y-intercept of a function is the point where the graph of the function crosses the y-axis. This occurs when the input x is equal to 0. To find the y-intercept, we need to evaluate the function at x = 0.Evaluate Option (A): Let's evaluate option (A) m(x) = 2x^2 + 16x + 24 at x = 0. m(0) = 2(0)^2 + 16(0) + 24 = 0 + 0 + 24 = 24 The y-intercept for option (A) is (0, 24).Evaluate Option (B): Now let's evaluate option (B) m(x) = 2(x + 4)^2 - 8 at x = 0. m(0) = 2(0 + 4)^2 - 8 = 2(4)^2 - 8 = 2(16) - 8 = 32 - 8 = 24 The y-intercept for option (B) is also (0, 24).Evaluate Option (C): Finally, let's evaluate option (C) m(x) = 2(x + 6)(x + 2) at x = 0. m(0) = 2(0 + 6)(0 + 2) = 2(6)(2) = 2 * 12 = 24 The y-intercept for option (C) is (0, 24) as well.Comparison: All three options give us the same y-intercept, (0, 24). However, the question asks which form most quickly reveals the y-intercept. The standard form (A) m(x) = 2x^2 + 16x + 24 directly shows the constant term +24, which is the y-intercept when x = 0. Therefore, option (A) most quickly reveals the y-intercept without any additional calculations or transformations.

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