Respuesta :
A quadratic function, when factored, is written as two binomials e.g. (x+2)(x-1), right? When we set each binomial equal to zero and solve, we get the x-intercepts of the graph...the zeros of the quadratic.
For this system, x=2 and x=9 are the zeros.
Therefore (x-2) and (x-9) are the binomials which solve to those zeros.
Multiply the binomials together to get the quadratic:
(x-2)(x-9) = x² - 11x + 18
f(x) = x² - 11x + 18
For this system, x=2 and x=9 are the zeros.
Therefore (x-2) and (x-9) are the binomials which solve to those zeros.
Multiply the binomials together to get the quadratic:
(x-2)(x-9) = x² - 11x + 18
f(x) = x² - 11x + 18
Substituting these values into the general form of a quadratic equation
f(x) = x² - 11x + 18
A quadratic equation is of the form:
f(x) = x² - (Sum of roots)x + (product of roots)
The given roots are 2 and 9
Sum of roots = 2 + 9
Sum of roots = 11
Product of roots = 2 x 9
Product of roots = 18
Substituting these values into the general form of a quadratic equation
f(x) = x² - 11x + 18
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