Mathematics: 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.

No number line is shown. To solve the inequality, add 5 to get -3x 3, and multiply by -1 (and remember to flip the sign!) to get 3x 3. Divide by 3 to get x 1....

Write an equation of a parabola that passes through

Ответ:

Soccermen1021

03.02.2022

Mathematics

The equation of the parabola is $y = \frac{2}{5}\cdot x^{2}-\frac{32}{5}\cdot x -\frac{72}{5}$ . 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:

$y = a\cdot x^{2}+b\cdot x + c$

Where:

- Independent variable, dimensionless.

- Dependent variable, dimensionless.

, , - Coefficients, dimensionless.

If we know that (3, -30) , (-2, 0) and (18, 0) are part of the parabola, the following linear system of equations is formed:

$9\cdot a +3\cdot b + c = -30$

$4\cdot a -2\cdot b +c = 0$

$324\cdot a +18\cdot b + c = 0$

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

$a = \frac{2}{5}$ , $b = -\frac{32}{5}$ , $c = -\frac{72}{5}$ .