Question

The function f, left bracket, x, right bracketf(x) is a quadratic function and the zeros of f, left bracket, x, right bracketf(x) are minus, 5−5 and 11. the y-intercept of f, left bracket, x, right bracketf(x) is 1010. write the equation of the quadratic polynomial in standard form.

Answer 1

The equation of the quadratic polynomial in standard form is f(x) = x² + 0.0211x - 0.0211. To find the equation, use the given zeros (-5 and 11) and the y-intercept (10). Substitute the zeros into the equation as factors and solve for the value of a using the y-intercept. Finally, substitute the value of a into the equation to get the quadratic polynomial in standard form.

Step-by-step explanation:

The equation of the quadratic polynomial in standard form is f(x) = x² + 0.0211x - 0.0211.

To find the equation, we use the given zeros (-5 and 11) and the y-intercept (10). Since the zeros of the quadratic function are -5 and 11, the factors are (x + 5) and (x - 11). Now, we can write the equation as f(x) = a(x + 5)(x - 11).

Next, substitute the y-intercept (10) into the equation to find the value of a. f(0) = 10, so (0 + 5)(0 - 11)a = 10. Solving this equation gives a = 1/2110.

Finally, substituting the value of a into the equation, we get the quadratic polynomial in standard form as f(x) = (1/2110)(x + 5)(x - 11) or f(x) = x² + 0.0211x - 0.0211.