Understanding the Basics of Quadratic Functions: Graphs, Intercepts, and Characteristics

quadratic function

A quadratic function is a type of function in algebra that can be written in the form f(x) = ax^2 + bx + c, where a, b, and c are constants, and x is the variable

A quadratic function is a type of function in algebra that can be written in the form f(x) = ax^2 + bx + c, where a, b, and c are constants, and x is the variable. The highest power of x in a quadratic function is 2, hence the name “quadratic.”

The graph of a quadratic function is a parabola, which can open upward or downward depending on the sign of the coefficient a. If a > 0, the parabola opens upward, and if a < 0, the parabola opens downward. The graph of a quadratic function typically has x-intercepts and a vertex. The x-intercepts are the points where the function crosses or touches the x-axis, and the vertex is the highest or lowest point on the parabola. The x-intercepts can be found by setting f(x) = 0 and solving the resulting quadratic equation. The vertex of a quadratic function can be found using the formula x = -b / (2a), and then substituting this value back into the original function to find the corresponding y-coordinate. The axis of symmetry of a quadratic function is a vertical line that passes through the vertex. It can be found using the equation x = -b / (2a). The y-intercept of a quadratic function is the point where the graph intersects the y-axis. It can be found by evaluating the function at x = 0, that is, calculating f(0). There are various properties and characteristics associated with quadratic functions, such as the domain and range, the vertex form (f(x) = a(x - h)^2 + k), and solving word problems using quadratic equations. These are just a few basics of quadratic functions, and there is much more to explore and learn about them.

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