Question

When x = 4 years, the number of houses in the city is 492. The number of houses in a city x years after 1960 is represented by the polynomial function c(x) = 3x² + 90x. To find the number of houses when x = 4 years, we simply substitute x with 4 in the function: c(4) = 3(4)² + 90(4) = 3(16) + 360 = 48 + 360 = 408. So, when x = 4 years after 1960, there are 408 houses in the city. Learn more about this polynomial function, which is a quadratic equation commonly used to model various real-world situations. Understanding how to evaluate such equations is fundamental in mathematics and data analysis.

Answer 1

A quadratic equation is a polynomial function of the form ax² + bx + c, used for modeling various real-world scenarios. To evaluate a quadratic equation, such as predicting the number of houses, substitute the value of x in the equation and solve. The quadratic formula is used to solve quadratic equations when they are set equal to zero.

Step-by-step explanation:

The student's question involves understanding the quadratic equation which is a second-order polynomial function commonly used in various real-world applications such as predicting the number of houses in a city. A quadratic function is usually of the form c(x) = ax² + bx + c, where a, b, and c are constants, and x represents the variable. Evaluating a quadratic function involves substituting the value of x into the equation and solving for c(x).

For example, given the quadratic function c(x) = 3x² + 90x, to find the number of houses when x represents the number of years after 1960, we substitute x = 4 to find c(4) = 3(4)² + 90(4), which simplifies to c(4) = 3(16) + 360 = 48 + 360 = 408 houses. Thus, according to this model, four years after 1960, there should be 408 houses in the city. The quadratic formula x = [-b ± √(b² - 4ac)]/(2a) is used to find the solutions of a quadratic equation when set equal to zero.