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
a) Solve the equation -(x+2)^2 + 9 = 0. Step 1: Isolate the squared term. -(x+2)^2 = -9 (x+2)^2 = 9 Step 2: Take the square root of both sides. x+2 = ±sqrt(9) x+2 = ±3 Step 3: Solve for x. For x+2 = 3: x = 3 - 2 x = 1 For x+2 = -3: x = -3 - 2 x = -5 The solutions are x=1 and x=-5. x=1, x=-5 b) The diagram shows a sketch of the graph of y = 3x^2 - 6x. The graph has its turning point at A. b)(i) Find the coordinates of C. Point C is an x-intercept, which means y=0. Set y=0 in the equation y = 3x^2 - 6x: 3x^2 - 6x = 0 Step 1: Factor out the common term. 3x(x - 2) = 0 Step 2: Set each factor to zero to find the x-intercepts. 3x = 0 x = 0 x - 2 = 0 x = 2 The graph shows that C is the x-intercept other than the origin. Therefore, the x-coordinate of C is 2. The coordinates of C are (2, 0). C=(2,0) b)(ii) Find the coordinates of A. Point A is the turning point (vertex) of the parabola y = 3x^2 - 6x. For a quadratic equation y = ax^2 + bx + c, the x-coordinate of the vertex is given by x = (-b)/(2a). In this equation, a=3, b=-6, and c=0. Step 1: Calculate the x-coordinate of the vertex. x = (-(-6))/(2(3)) x = (6)/(6) x = 1 Step 2: Substitute the x-coordinate back into the equation to find the y-coordinate. y = 3(1)^2 - 6(1) y = 3(1) - 6 y = 3 - 6 y = -3 The coordinates of A are (1, -3). A=(1,-3) Send me the next one 📸