Given the quadratic function f (a) = d^2 - 7d + 6
Factor the equation into a binomial product.
Solve for the roots of the equation.
This quadratic function models the path, height in feet as a function of distance in
feet, that a diver takes when they dive from a platform at the edge of a pool. How far away will the diver be from the edge of the pool when they return to the surface?
To factor the equation, we need to find two numbers that multiply to 6 and add up to -7. These numbers are -1 and -6. Therefore, the factored form of the equation is:
f(a) = (d-1)(d-6)
To find the roots of the equation, we set f(a) to zero and solve for d:
0 = (d-1)(d-6)
d = 1 or d = 6
Therefore, the roots of the equation are d = 1 and d = 6.
To find how far away the diver will be from the edge of the pool when they return to the surface, we need to find the distance they traveled. This is the difference between the two roots:
distance = 6 - 1 = 5 feet
Therefore, the diver will be 5 feet away from the edge of the pool when they return to the surface.