Demystifying Quadratic Parent Functions | Characteristics, Properties, and Transformation Analysis

Graph of Quadratic Parent Function

The graph of a quadratic parent function is a U-shaped curve called a parabola

The graph of a quadratic parent function is a U-shaped curve called a parabola. The general form of a quadratic equation is f(x) = ax^2 + bx + c, where a, b, and c are constants and a cannot be equal to zero.

The graph of a quadratic parent function has the following characteristics:

1. Vertex: The highest or lowest point on the graph, which is also the point where the parabola changes direction. It can be found using the formula x = -b/2a. The y-coordinate of the vertex can be calculated by substituting the x-coordinate into the quadratic equation.

2. Axis of Symmetry: A vertical line that passes through the vertex and divides the parabola into two symmetric halves.

3. Roots or Zeros: The x-values for which the quadratic equation equals zero. These are the points where the parabola intersects the x-axis. The roots can be found by solving the quadratic equation ax^2 + bx + c = 0 using factoring, the quadratic formula, or completing the square.

4. y-intercept: The point where the parabola intersects the y-axis. The y-intercept can be found by substituting x = 0 into the quadratic equation, resulting in f(0) = c.

5. Direction: The direction of the parabola is determined by the coefficient ‘a’. If ‘a’ is positive, the parabola opens upward, and if ‘a’ is negative, the parabola opens downward.

The shape, position, and orientation of the graph of a quadratic parent function may be altered by applying transformations, such as translations, reflections, stretches, and compressions. These transformations can shift the parabola vertically or horizontally, change its scale, or flip it upside down.

By understanding the characteristics and properties of a quadratic parent function, you can analyze and graph various quadratic equations by applying the appropriate transformations.

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