Answer :
Answer:
y = x² - 9x + 14
Step-by-step explanation:
Given the zeros x = 7 and x = 2, then the corresponding factors are
(x - 7) and (x - 2)
The function is then the product of its factors, that is
y = (x - 7)(x - 2) ← expand using FOIL
= x² - 9x + 14
The quadratic function with zeros 7 and 2 in standard form is
f(x) = x² - 9x + 14
If a quadratic function has zeros of a and b, then the quadratic function can be formed as:
f(x) = (x - a)(x - b)
For a function with zeros 7 and 2:
a = 7, b = 2
Substitute a = 7 and b = 2 into the quadratic function f(x) = (x - a)(x - b)
f(x) = (x - 7)(x - 2)
Expand the expression
f(x) = x² - 2x - 7x + 14
f(x) = x² - 9x + 14
The quadratic function with zeros 7 and 2 in standard form is f(x) = x² - 9x + 14
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