To find the equation of a quadratic function with given zeros, we can use the formula f(x) = a(x - a)(x - b), where a and b are the zeros. For x=2 and x=-5, the equation is f(x) = (x-2)(x+5), which can be expanded to f(x) = x^2 + 3x - 10. ;
The quadratic function with zeros at x = 2 and x = -5 is f(x) = (x - 2)(x + 5).
f(x) = x² + 3x - 10.
First, write the function in factored form:
f(x) = (x - 2)(x + 5)
Next, expand this product to find the standard form,
*f(x) = (x - 2)(x + 5) = x 2 + 5 x − 2 x − 10 * = x 2 + 3 x − 10
Therefore, the equation of the quadratic function in standard form is:
f(x) = x² + 3x - 10
The equation of the quadratic function with zeros at x = 2 and x = − 5 can be expressed in standard form as f ( x ) = x 2 + 3 x − 10 . This was determined by expanding the factored form of the quadratic function. Combining like terms gave us the standard expression for the quadratic function.
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