Let’s dive into the world of quadratic functions! The equation you provided, , represents a parabola that opens upwards because the coefficient in front of (which is 4) is positive. You can find the vertex, which represents the highest or lowest point on the graph, using the formula . Here, substituting and will reveal that the vertex’s x-coordinate is -1.

Now, to see this equation in action, consider its applications in areas such as physics, where quadratic functions can describe the motion of objects under the influence of gravity. For example, if you throw a ball into the air, its trajectory can be modeled by a quadratic equation like yours. By analyzing the function, you can determine the ball’s maximum height and how long it’ll take to hit the ground!