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zhuklara
8 days ago
6

What is the equation of the quadratic function with a vertex at (2,-25) and an x-intercept at (7,0)?

Mathematics
1 answer:
AnnZ [9K]8 days ago
8 0
The quadratic function can be expressed as f(x) = (x + 3)(x - 7). To derive this, utilize the "standard form" and incorporate the provided points: vertex at (2, -25) and intercept at (7, 0). Starting from f(x) = a(x-h)² + k, with h set to 2 and y equal to -25, and substituting x as 7 to solve for a gives us 0 = a(7-2)² - 25. This implies 25 = 25a, thus a is found to be 1. Using the standard form leads to f(x) = (x-2)² - 25, expanding (x-2)² as x² - 4x + 4. Simplifying this results in f(x) = x² - 4x - 21, which can then be factored to yield f(x) = (x + 3)(x - 7).
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