The height, h, in feet, of a baseball t seconds after Tobin hit it with a baseball bat can be modeled by the equation: h(t)=-16t^(2)+64 t+4 Which of the following equivalent expressions displays the value of the baseball's maximum height as a constant or coefficient? Choose 1 answer: (A) -16(t-2)^(2)+68 (B) -4t(4t-16)+4 (C) -16(t^(2)-4t-(1)/(4)) (D) -16(t^(˙)^(2)-4t)+4

Question

The height,  h, in feet, of a baseball  t seconds after Tobin hit it with a baseball bat can be modeled by the equation:  h(t)=-16t^(2)+64 t+4 Which of the following equivalent expressions displays the value of the baseball's maximum height as a constant or coefficient? Choose 1 answer: (A)  -16(t-2)^(2)+68 (B)  -4t(4t-16)+4 (C)  -16(t^(2)-4t-(1)/(4)) (D)  -16(t^(˙)^(2)-4t)+4

Bytelearn · Accepted Answer

Problem Understanding: Understand the problem. We are given the quadratic equation h(t) = -16t^2 + 64t + 4, which models the height of a baseball t seconds after being hit. We need to find an equivalent expression that shows the maximum height of the baseball as a constant or coefficient.Quadratic Equation Structure: Recognize the structure of the quadratic equation. The given equation is in the standard form of a quadratic equation, which is h(t) = at^2 + bt + c. The maximum height of the baseball will occur at the vertex of the parabola represented by this quadratic equation.Finding Time of Maximum Height: Find the time at which the maximum height occurs. The time at which the maximum height occurs can be found using the formula t = -b/(2a), where a is the coefficient of t^2 and b is the coefficient of t in the quadratic equation. For our equation, a = -16 and b = 64, so t = -64/(2 * -16) = 2 seconds.Writing Equation in Vertex Form: Write the equation in vertex form. The vertex form of a quadratic equation is h(t) = a(t - h)^2 + k, where (h, k) is the vertex of the parabola. Since we know the time of the maximum height is 2 seconds, we can write the equation as h(t) = -16(t - 2)^2 + k.Calculating Maximum Height: Calculate the maximum height k. To find the value of k, we substitute t = 2 into the original equation h(t) = -16t^2 + 64t + 4. h(2) = -16(2)^2 + 64(2) + 4 = -64 + 128 + 4 = 68 feet. So, the maximum height k is 68 feet.Final Vertex Form Equation: Write the final vertex form equation. Now that we have the value of k, we can write the final vertex form equation as h(t) = -16(t - 2)^2 + 68.Matching with Given Choices: Match the final vertex form equation with the given choices. The final vertex form equation we found is h(t) = -16(t - 2)^2 + 68, which matches choice (A).

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