SOLUTION: A cliff diver’s height above the water, in meters, is modeled by the function ℎ(𝑑) = −𝑑^2 + 2𝑑 + 24, where d represents how far the diver is

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: A cliff diver’s height above the water, in meters, is modeled by the function ℎ(𝑑) = −𝑑^2 + 2𝑑 + 24, where d represents how far the diver is       Log On


   

Question 1129023: A cliff diver’s height above the water, in
meters, is modeled by the function
ℎ(𝑑) = −𝑑^2 + 2𝑑 + 24, where d represents
how far the diver is from the cliff. How far
from the cliff will the diver be when she
reaches the water?
A. 0 meters
B. 4 meters
C. 6 meters
D. 24 meters
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The maximum height, +h%5Bmax%5D+ is where
the diver starts. This is the vertex of a parabola
+d%5Bv%5D+=+-b%2F%282a%29+
+a+=+-1+
+b+=+2+
+d%5Bv%5D+=+-2%2F%282%2A%28-1%29%29+
+d%5Bv%5D+=+1+
+h%281%29+=+-1%5E2+%2B+2%2A1+%2B+24+
+h%281%29+-1+%2B+2+%2B+24+
+h%281%29+=+25+
--------------------
Find +h%28d%29+=+0+
+-d%5E2+%2B+2d+%2B+24+=+0+
+%28+d+%2B+4+%29%2A%28-+d+%2B+6+%29+=+0+
+d+=+6+
C. 6 meters is the answer I get.
Here's the plot:
+graph%28+400%2C+400%2C+-7%2C+7%2C+-4%2C+30%2C+-x%5E2+%2B+2x+%2B+24%29+
The diver has to start at +d=0+. It looks like the
diver then jumps up 1 meter to 25 m above the water
and hits the water 6 m form the cliff.