The standard form of the equation of the parabola is y + 3 = (1/3) · (x - 3)² and The factored form of the equation of the parabola is y = (1/3) · x · (x - 6).
How to derive the two forms of the equation of the parabola
Mathematically speaking, parabolae are defined by second order polynomials. The standard form of the equation of the parabola is defined by:
y - k = C · (x - h)² (1)
Where C is the vertex constant.
And the factored form has this form:
y = k · (x - r₁) · (x - r₂) (2)
First, we determine the standard form of the equation of the parabola: (h, k) = (3, - 3) and (x, y) = (0, 0)
0 - (- 3) = C · (0 - 3)²
3 = 9 · C
C = 1/3
Then, the standard form of the equation of the parabola is y + 3 = (1/3) · (x - 3)². Now we proceed to determine the factored form of the parabola: (r₁ = 0, r₂ = 6), (h, k) = (3, - 3)
- 3 = k · (3 - 0) · (3 - 6)
- 3 = k · 3 · (- 3)
- 3 = - 9 · k
k = 1/3
The factored form of the equation of the parabola is y = (1/3) · x · (x - 6).
To learn more on quadratic equations: https://brainly.com/question/17177510
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