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
The given equation is y = x^2 - 4x. Step 1: Find the coordinates of points B and C. Points B and C are the x-intercepts, where the graph crosses the x-axis. At these points, y=0. Set y=0 in the equation: x^2 - 4x = 0 Factor out x: x(x - 4) = 0 This gives two possible values for x: x = 0 or x - 4 = 0 x = 4 So, the x-intercepts are (0, 0) and (4, 0). From the graph, point B is the origin and point C is the other intercept. The coordinates are: B: (0, 0) C: (4, 0) Step 2: Find the minimum value of y. The equation y = x^2 - 4x is a parabola opening upwards (since the coefficient of x^2 is positive). Its minimum value occurs at the vertex (turning point). The x-coordinate of the vertex for a quadratic equation y = ax^2 + bx + c is given by x = -(b)/(2a). In our equation, a=1 and b=-4. x = -(-4)/(2(1)) = (4)/(2) = 2 Now, substitute this x-value back into the equation to find the minimum y-value: y = (2)^2 - 4(2) y = 4 - 8 y = -4 The minimum value of y is -4. Step 3: Find the coordinates of the turning point. The turning point is the vertex of the parabola. From Step 2, we found the x-coordinate of the vertex is x=2 and the corresponding y-value (minimum value) is y=-4. The coordinates of the turning point are (2, -4). Send me the next one 📸