If a point on the pre-image has coordinates (3.-4), and the coordinates of Its Image are (12,-16), what scale factor was
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Answer:
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.