Intermediate Algebra | 34.3: Graphing Parabolas: Vertex and Intercepts
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Learn a reliable six-step method for graphing any quadratic function by plotting three key features in a specific order. This video shows how to find the vertex, y-intercept, and x-intercepts, then how to connect them into a smooth parabola using symmetry — with two fully worked examples.
Key concepts covered:
• Three key features: vertex (highest or lowest point), y-intercept (always exists), and x-intercepts (0, 1, or 2)
• Plotting order: vertex first as the structural anchor, y-intercept second, x-intercepts last
• Vertex formula: x = −b/(2a), then substitute back to find the y-coordinate
• Y-intercept equals the constant term C
• Finding x-intercepts by setting the function equal to zero and factoring
• How the sign of A determines whether the parabola opens upward (positive A) or downward (negative A)
• Drawing smooth, rounded curves — avoiding the common mistakes of straight line segments and sharp corners at the vertex
• Using the axis of symmetry to mirror the curve and complete the graph
• Worked examples: y = x² − 4x − 5 and y = x² − 2x − 3