Question

a quadratic function f(x) is hidden from view. you must find the x-intercept(s) of f(x) and write the answer(s) in the form (x, y). choose the form of the quadratic function f(x) that you would like to see in order to answer the question most efficiently. form: standard form f(x) = -x² + 10x - 16 answer attempt 1 out of 2 there are no x-intercepts there are no x-intercepts there is one x-intercept there are two x-intercepts

Explanation:

Step1: Recall x-intercept definition

To find x-intercepts, set \( y = f(x) = 0 \), so solve \( -x^2 + 10x - 16 = 0 \). Multiply both sides by -1: \( x^2 - 10x + 16 = 0 \).

Step2: Factor the quadratic

Factor \( x^2 - 10x + 16 \). Find two numbers that multiply to 16 and add to -10: -2 and -8. So, \( (x - 2)(x - 8) = 0 \).

Step3: Solve for x

Set each factor to 0: \( x - 2 = 0 \) gives \( x = 2 \); \( x - 8 = 0 \) gives \( x = 8 \). At x-intercepts, \( y = 0 \), so the points are \( (2, 0) \) and \( (8, 0) \). Thus, there are two x-intercepts.

Answer:

There are two x - intercepts, and the x - intercepts are \((2, 0)\) and \((8, 0)\)