Write an equation of a parabola that passes through (3,-30) and has x-intercepts of -2 and 18. Then find the average rate of change from x= -2 to x=8.

The equation of the parabola is .  The average rate of change of the parabola is -4.

Step-by-step explanation:

We must remember that a parabola is represented by a quadratic function, which can be formed by knowing three different points. A quadratic function is standard form is represented by:

Where:

- Independent variable, dimensionless.

- Dependent variable, dimensionless.

, , - Coefficients, dimensionless.

If we know that , and are part of the parabola, the following linear system of equations is formed:

This system can be solved both by algebraic means (substitution, elimination, equalization, determinant) and by numerical methods. The solution of the linear system is:

, , .

The equation of the parabola is .

Now, we calculate the average rate of change (), dimensionless, between and by using the formula of secant line slope:

The average rate of change of the parabola is -4.

7

step-by-step explanation: