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
Part (a): Step 1: Set the given expression for y equal to -2. (1 - 2x)(1 + x) - 2 = -2 Step 2: Add 2 to both sides of the equation. (1 - 2x)(1 + x) = 0 Step 3: Solve for x by setting each factor to zero. 1 - 2x = 0 2x = 1 x = (1)/(2) 1 + x = 0 x = -1 The values of x are x = (1)/(2) or x = -1. Part (b): The function is y = x(x - 2). b)(i) Find the coordinates of the points where the curve cuts the x-axis. Step 1: The curve cuts the x-axis when y = 0. Set the function equal to zero. x(x - 2) = 0 Step 2: Solve for x. x = 0 or x - 2 = 0 x = 2 Step 3: Write the coordinates. The coordinates are (0, 0) and (2, 0). b)(ii) What is the maximum value of the function? The function is y = x(x - 2) = x^2 - 2x. This is a parabola that opens upwards (since the coefficient of x^2 is positive). Therefore, it has a minimum value, not a maximum value (the function increases indefinitely towards positive infinity). Assuming the question meant to ask for the minimum value: Step 1: Find the x-coordinate of the vertex, which is where the minimum occurs. For a quadratic y = ax^2 + bx + c, the x-coordinate of the vertex is x = -(b)/(2a). Here, a=1 and b=-2. x = -(-2)/(2(1)) = (2)/(2) = 1 Step 2: Substitute this x-value back into the function to find the minimum y-value. y = (1)^2 - 2(1) = 1 - 2 = -1 The minimum value of the function is -1. That's 2 down. 3 left today — send the next one.