3) Draw a graph of a quadratic function \( y=x^{2} \), labelling the axes and at least 3 points.

To properly draw the graph of the quadratic function \( y = x^{2} \), start by labeling your axes as the x-axis (horizontal) and the y-axis (vertical). The curve will be a U-shaped parabola that opens upwards. Plot at least three key points: 1. When \( x = -2 \), \( y = (-2)^{2} = 4 \) (point at (-2, 4)). 2. When \( x = 0 \), \( y = 0^{2} = 0 \) (point at (0, 0)). 3. When \( x = 2 \), \( y = (2)^{2} = 4 \) (point at (2, 4)). Highlight these points and sketch a smooth curve through them to complete your graph. Remember that the vertex is at the origin, and the symmetrical nature of the parabola makes plotting easy! The quadratic function has been around for centuries, with roots tracing back to ancient civilizations like the Babylonians who used a form of it for solving areas and problems involving squares. The term "quadratic" itself comes from the Latin word "quadratus," meaning square, reflecting the function's squared nature! This shows how maths has evolved while remaining relevant from ancient times to today. In real-world applications, quadratic functions represent various phenomena, such as projectile motion, where the path of an object in flight can be modeled by a parabolic graph. For instance, when you throw a ball, its height over time can be depicted by a quadratic function, enabling scientists and engineers to calculate trajectories and optimize performance in sports and vehicle launches! This connection between maths and motion can add excitement to your studies!