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
Here's how to determine the features of the quadratic function y = 8 - 2x^2: 1.4.1 x-intercepts To find the x-intercepts, set y=0 and solve for x. 0 = 8 - 2x^2 Add 2x^2 to both sides: 2x^2 = 8 Divide by 2: x^2 = 4 Take the square root of both sides: x = ±sqrt(4) x = ± 2 The x-intercepts are at (-2, 0) and (2, 0). x = -2 and x = 2 1.4.2 Axis of symmetry For a quadratic function in the form y = ax^2 + bx + c, the axis of symmetry is given by x = -(b)/(2a). In the equation y = 8 - 2x^2, we can write it as y = -2x^2 + 0x + 8. So, a = -2, b = 0, and c = 8. x = -(0)/(2(-2)) x = 0 The axis of symmetry is the y-axis. x = 0 1.4.3 Turning point The x-coordinate of the turning point is the axis of symmetry, which is x=0. Substitute x=0 into the equation to find the y-coordinate: y = 8 - 2(0)^2 y = 8 - 0 y = 8 The turning point is (0, 8). (0, 8) 1.4.4 Sketch the graph To sketch the graph of y = 8 - 2x^2: • It is a parabola opening downwards because the coefficient of x^2 (which is -2) is negative. • The x-intercepts are at (-2, 0) and (2, 0). • The y-intercept is found by setting x=0, which gives y = 8 - 2(0)^2 = 8. So, the y-intercept is (0, 8). This is also the turning point. • Plot these three points and draw a smooth parabolic curve through them, opening downwards. 3 done, 2 left today. You're making progress.