By rewriting the function into graphing form, we can identify the vertex.
B
b
Consider the y-intercept and vertex.
A
a
Sketch:
B
b
Start of jump: 400 feet
Maximum height: 404 feet
Practice makes perfect
a
In any function, the constant shows the y-intercept. Therefore, when examining the function, we can identify the y-intercept as 400.
h=-16t^2+16t+ 400 ← constant
We will start by plotting the y-intercept.
To find the vertex of the function, we should rewrite it into graphing form.
Graphing Form:& y=a(x- h)^2+ k
Vertex:& ( h, k)
To do that we have to complete the square. However, this requires the squared variable to have a coefficient of 1. Therefore, we will first divide both sides of the equation by - 16.
h=- 16t^2+16t+400
⇓
h/- 16=t^2-t-25
Now we can complete the square and thereby write the function in graphing form.
The function has a vertex at ( 12,404). With this information, we can graph the function.
b
The diver starts his jump when t=0. From Part A we know that the y-intercept was 400, which means the diver started his jump 400 feet above the water. We also determined that the function's vertex is (0.5,404), which is the function's maximum value. Therefore, the maximum height is 404 feet.
