Question

apply math models the height of imani's mid-section was measured three times during a long jump. time in seconds, x height in meters, у 0.7 0.5 1.5 1 0.55 h = 1.5 meters write the equation of a quadratic function that describes imani's height as a function of time.

Answer 1

To find the equation of a quadratic function that describes Imani's height as a function of time, we can use the three measurements provided. The equation is h(t) = -0.96t^2 + 2.945t + 0.605.

Step-by-step explanation:

To find the equation of a quadratic function that describes Imani's height as a function of time, we can use the three measurements provided. The given time values are 0.7, 1.5, and 0.55 seconds, and the corresponding height values are 0.5, 1, and 0.55 meters. We can use these points to form a quadratic equation in the form: h(t) = at^2 + bt + c. Substituting the values we have, we get the following system of equations: 0.5 = 0.49a + 0.7b + c, 1 = 2.25a + 1.5b + c
0.55 = 0.3025a + 0.55b + c. Solving these equations simultaneously, we find that a = -0.96, b = 2.945, and c = 0.605. Therefore, the equation that describes Imani's height as a function of time is h(t) = -0.96t^2 + 2.945t + 0.605.