Praxis Core Academic Skills for Educators: Mathematics (5733)Algebra and FunctionsEasy
A civil engineer is designing a road that passes over a hill. The height of the road, h(x), in meters above sea level, can be modeled by the polynomial function h(x) = -0.01x³ + 0.5x² - 3x + 100, where x is the horizontal distance in kilometers from a reference point. What is the height of the road at the reference point (x = 0)?
- A100 meters
- B0 meters
- C0.5 meters
- D3 meters
Show answer & explanationAnswer & explanation
Correct answer: A. 100 meters
To find the height at the reference point (x = 0), substitute x = 0 into the function h(x). All terms containing 'x' will become zero, leaving only the constant term.
Why the other options are wrong
- B. This would be true if the constant term was 0, but it is 100.
- C. This is the coefficient of the x² term, not the value when x=0.
- D. This is the coefficient of the x term, not the value when x=0.
Evaluating Polynomials at x=0
When a polynomial function is evaluated at x=0, the result is always the constant term of the polynomial.
- All terms with 'x' become zero.
- The constant term is the y-intercept.
- It represents the initial value or starting point when x signifies time or distance.
Memory trick: Plug in value, then calculate sums.