The equation of the parabola is f(x) = - 2 · (x + 3) · (x - 1).
How to define the equation of a parabola
In this problem we find the graph of a parabola, whose definition is a quadratic equation, whose definition is introduced below:
f(x) = a · (x - r₁) · (x - r₂)
Where:
- a - Lead coefficient
- r₁, r₂ - Roots
Please notice that roots are the points of the quadratic equation that pass through x-axis. The lead coefficient can be found easily based on y-intercept, that is, the point of the parabola pass through y-axis.
First, determine the lead coefficient of the parabola: (r₁ = - 3, r₂ = 1)
6 = a · (0 + 3) · (0 - 1)
6 = - 3 · a
a = - 2
Second, write the complete quadratic equation:
f(x) = - 2 · (x + 3) · (x - 1)