By the vertex form of the parabola, the equation of the parabola shown in the diagram is equal to the quadratic equation y - 1 = (2/3) · (x - 3)².
How to determine the equation of the parabola in vertex form
Parabolae are represented mathematically by second order polynomials, which can be described either in standard form or in vertex form. In accordance to the picture, we have a parabola with a vertical axis of symmetry. The formula in vertex form is described by this expression:
y - k = C · (x - h)²
Where:
- (h, k) - Coordinates of the vertex.
- C - Vertex constant
Please notice that vertices represent the absolute extreme of the parabola. We can determine the equation by knowing the vertex and another point. Let be (h, k) = (3, 1) and (x, y) = (0, 7), then we find that the vertex constant is:
7 - 1 = C · (0 - 3)²
6 = 9 · C
C = 2/3
By the vertex form of the parabola, the equation of the parabola shown in the diagram is equal to the quadratic equation y - 1 = (2/3) · (x - 3)².
To learn more on parabolae: https://brainly.com/question/21685473
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