Determine which of the graphs-a), b), or c)

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Key Concepts

Intercepts

Intercepts are the points where the graph crosses the axes. The y-intercept is found directly from the constant c in the equation, while the x-intercepts (or roots) are determined by solving the equation ax² + bx + c = 0. These intercept points are key features used to sketch and recognize the graph of a quadratic function.

Vertex and Axis of Symmetry

The vertex of a parabola is its highest or lowest point, serving as a turning point, and it can be found using the formula x = -b/(2a). This vertex lies on the axis of symmetry, a vertical line that divides the parabola into two mirror-image halves, providing crucial information about the graph's position and orientation.

Parabolic Shape

The graph of a quadratic function is a parabola, a symmetric curve that opens upward if the coefficient a is positive and downward if a is negative. Recognizing the parabolic shape is essential for identifying the type of graph that represents a given quadratic equation.

Quadratic Functions

Quadratic functions are polynomial functions of degree two, commonly written in the standard form y = ax² + bx + c. They always graph as parabolas and are fundamental in algebra and calculus for studying curves, optimization, and solving problems involving maximum and minimum values.

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