Noah is designing a new ride for an amusement park called the Pendulum Plunge. Riders in a padded, enclosed "car" will be released from a certain height and rapidly swung through the air. Noah uses the function p(x)=x^2-16x+84 to define the height of the "car" x seconds after the ride begins .the form of p (x) that best reveals its vertex is . the vertex of p(x) is
To reveal the vertex of the function p(x) = x^2 - 16x + 84, we first need to rewrite the function in vertex form: p(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.
First, complete the square to convert the function into vertex form:
p(x) = x^2 - 16x + 64 + 84 - 64
p(x) = (x - 8)^2 + 20
Now we can see that the vertex of the parabola is at (h, k) = (8, 20). This means that the height of the "car" will reach its maximum point at 20 units after 8 seconds into the ride.
Select the appropriate word(s) or value from each drop-down menu to correctly complete the statement.
the vertex for p(x) indicates that the function will reach a
(maximum height,minimum height,minimum elapsed time ,maximum elapsed time ) of (12 seconds,12 feet,20 seconds, 20 feet , 84 seconds , 84 feet ) exactly (4 seconds , 7 seconds , 8 seconds , 16 seconds ) after the ride begins