Determine the maximum height of the projectile modeled by h(t) = -16t^2 + 64t +
Practice Questions
Q1
Determine the maximum height of the projectile modeled by h(t) = -16t^2 + 64t + 80. (2020)
80
64
48
96
Questions & Step-by-Step Solutions
Determine the maximum height of the projectile modeled by h(t) = -16t^2 + 64t + 80. (2020)
Step 1: Identify the equation of the projectile's height, which is h(t) = -16t^2 + 64t + 80.
Step 2: Recognize that this is a quadratic equation in the form h(t) = at^2 + bt + c, where a = -16, b = 64, and c = 80.
Step 3: To find the time t at which the maximum height occurs, use the formula t = -b/(2a).
Step 4: Substitute the values of a and b into the formula: t = -64/(2 * -16).
Step 5: Calculate the denominator: 2 * -16 = -32, so t = -64 / -32 = 2.
Step 6: Now that we have t = 2, substitute this value back into the height equation to find the maximum height: h(2) = -16(2^2) + 64(2) + 80.
Step 7: Calculate 2^2, which is 4, then multiply: -16 * 4 = -64.
Step 8: Calculate 64 * 2, which is 128.
Step 9: Now combine the results: h(2) = -64 + 128 + 80.
Step 10: Add these values together: -64 + 128 = 64, then 64 + 80 = 144.
Step 11: Therefore, the maximum height of the projectile is 144.
Quadratic Functions – Understanding the properties of quadratic functions, including how to find the vertex which represents the maximum or minimum value.
Vertex Formula – Using the vertex formula t = -b/(2a) to find the time at which the maximum height occurs.
Substitution – Substituting the value of t back into the height function to find the maximum height.
