Quadratic Function Graph
A quadratic function graph represents the relationship between a quadratic equation and its corresponding graph on a coordinate plane
A quadratic function graph represents the relationship between a quadratic equation and its corresponding graph on a coordinate plane. A quadratic function is a polynomial of degree 2, and it can be written in the form of f(x) = ax^2 + bx + c, where a, b, and c are constants.
When graphing a quadratic function, there are a few key points to consider:
1. Vertex: The vertex is the lowest or highest point on the graph, depending on the direction of the parabola. It can be found using the formula x = -b / 2a. The y-coordinate of the vertex can be obtained by substituting this x-value into the equation.
2. Axis of Symmetry: The axis of symmetry is a vertical line that divides the parabola into two symmetric parts. The equation for the axis of symmetry is given by x = -b / 2a. It passes through the vertex.
3. Intercepts: The x-intercepts are the points at which the graph of the quadratic function crosses or touches the x-axis. To find the x-intercepts, set f(x) to zero and solve the quadratic equation for x. The y-intercept is the point where the graph intersects the y-axis. To find the y-intercept, substitute x = 0 into the equation.
4. Shape of the Parabola: The shape of the parabola depends on the leading coefficient (a) of the quadratic equation. If a > 0, the parabola opens upwards, and if a < 0, it opens downwards. To sketch the graph of a quadratic function, follow these steps: 1. Find the vertex, axis of symmetry, and intercepts as described above. 2. Plot these key points on a coordinate plane. 3. Draw a smooth curve passing through the vertex and symmetric around the axis of symmetry. 4. Label the graph with any other important points, such as the maximum or minimum values. It's important to remember that each quadratic function will have its unique graph, and the behavior of the graph can vary depending on the values of the constants a, b, and c. By analyzing the key points on the graph, you can determine various properties of the quadratic function, such as the direction of the parabola, the maximum or minimum value (if applicable), the range, and the domain.
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