How many times does the graph of 4x = 32 - x2 cross the x-axis?012

Answer:2Step-by-step explanation:4x = 32 - x2 would be much clearer if written as 4x = 32 - x^2.  Please use" ^ " to indicate exponentiation.Rewrite 4x = 32 - x^2 in the standard form of a quadratic:  x^2 + 4x - 32Then the coefficients are a = 1, b = 4 and c = -32.Find the discriminant.  It is b^2-4ac.  Here, b^2-4ac = 4^2 - 4(1)(-32), or 16 + 128, or 144.Because the discriminant is positive, we know immediately that this quadratic has two real, unequal roots.So, the answer to this question is "the graph of 4x = 32 - x^2 cross the x-axis in two places."