This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To find the critical values where the two functions f(x) = x^2 and g(x) = x+2 intersect, you need to set them equal to each other and solve for x. Step 1: Set f(x) equal to g(x). f(x) = g(x) x^2 = x+2 Step 2: Rearrange the equation into a standard quadratic form (ax^2 + bx + c = 0). Subtract x and 2 from both sides: x^2 - x - 2 = 0 Step 3: Solve the quadratic equation for x. You can solve this by factoring, using the quadratic formula, or completing the square. Factoring is often the quickest method if possible. We need two numbers that multiply to -2 and add to -1. These numbers are -2 and 1. (x-2)(x+1) = 0 Step 4: Set each factor equal to zero and solve for x. x-2 = 0 x = 2 x+1 = 0 x = -1 The critical values (x-coordinates of the intersection points) are x = 2 and x = -1. What's next?