f the distance the car traveled after applying the brakes equals 20 feet, what does that mean to the officer investigating the accident? (HINT: Let d = 20, bring 20 to the right so that the equation equals zero, identify the coefficients, A, B and C and then use the quadratic formula to solve mathematically.)
To understand what the distance the car traveled after applying the brakes means to the investigating officer, we need to solve the equation related to the situation using the quadratic formula.
Let's start with the equation and the given information. The equation is in the form of a quadratic equation: Ax^2 + Bx + C = 0, where x represents the unknown distance.
Given: The distance the car traveled after applying brakes equals 20 feet, so we can write the equation as x^2 - 20 = 0.
To use the quadratic formula, we need to identify the coefficients A, B, and C in the equation.
A = coefficient of x^2 term = 1 (since there is no coefficient explicitly written)
B = coefficient of x term = 0 (since there is no x term in the equation)
C = constant term = -20
So the quadratic equation becomes: x^2 + 0x - 20 = 0.
Now, let's apply the quadratic formula to solve for x:
The quadratic formula is: x = (-B ± √(B^2 - 4AC)) / (2A)
Plugging in the values, we get: x = (0 ± √(0^2 - 4(1)(-20))) / (2(1))
Simplifying further: x = ± √(0 + 80) / 2
x = ± √80 / 2
x = ± √(16 * 5) / 2
x = ± (4√5) / 2
x = ± 2√5
So the solutions for x are x = 2√5 and x = -2√5.
Now, let's interpret these solutions in the context of the investigating officer:
The positive solution, x = 2√5, represents the distance the car traveled after applying brakes in a positive direction.
The negative solution, x = -2√5, represents the distance the car traveled after applying brakes in a negative (or backward) direction.
Therefore, if the distance the car traveled after applying the brakes equals 20 feet, it means that the officer investigating the accident found that the car traveled either 2√5 feet in a forward direction or -2√5 feet in a backward direction after the brakes were applied.