A rock is thrown from a height of 48 feet.
Solving the quadratic equation -16x² + 32x + 48=0 will give the time, x, when the rock hits the ground.
Assume the rock is thrown when x = 0.
Use the graph of the equation to decide if each zero is a solution to this problem.
a) both zeros are solutions to this problem
b) neither zeros are a solution to this problem
c) only -1 is a solution to this problem
d) only 3 is a solution to this problem
To find the solutions to the quadratic equation -16x² + 32x + 48 = 0, we can factor it or use the quadratic formula. Factoring the equation, we get:
-16x² + 32x + 48 = 0
-16(x² - 2x - 3) = 0
-16(x - 3)(x + 1) = 0
So the solutions to the equation are x = 3 and x = -1.
To decide if each zero is a solution to this problem (representing the time when the rock hits the ground), we can plug in these values into the quadratic equation and see if the equation holds true.
For x = 3:
-16(3)² + 32(3) + 48 = 0
-16(9) + 96 + 48 = 0
-144 + 96 + 48 = -48
Since the equation does not hold true for x = 3, it is not a solution to this problem.
For x = -1:
-16(-1)² + 32(-1) + 48 = 0
-16(1) - 32 + 48 = 0
-16 - 32 + 48 = 0
The equation holds true for x = -1, so it is a solution to this problem.
Therefore, the correct answer is c) only -1 is a solution to this problem.