What is the equation of the quadratic function with a vertex at (2.-25) and an x-intercept at (7.0)?

fix) = (x - 2)(x - 7)

fx) = (x + 2)(x + 7)

fx) = (x - 3)(x + 7)

fix) = (x+3)(x-7)

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Step-by-step explanation:

According to the statement, the quadratic function (parabola) has the following form:

The standard form is unleashed after expading the algebraic equation:

The zeroes of the second-order polynomial are contained in this expression:

Given that and assuming a positive sign, the value of C is finally found:

(since vertex is a minimum).

The remaining zero of the polynomial is:

Therefore, the polynomial is .

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis: