Quadratics Summary

Algebra 1 · Axiom Academy

SUMMARY Quadratic Functions and Equations A review of the key ideas for understanding parabolas and solving quadratic equations. Quadratic functions graph as parabolas — U-shaped curves defined by a vertex, an axis of symmetry, and their intercepts. The same quadratic can be written three ways — standard , vertex , and factored form — each exposing a different feature. There are three ways to solve a quadratic equation: factoring , completing the square , and the quadratic formula . The discriminant b^2 - 4ac tells you how many real solutions there are before you solve. The quadratic formula works for every quadratic equation, no factoring required. Core Concept Understanding Parabolas A quadratic function graphs as a U-shaped curve called a parabola that opens upward or downward. Vertex: the highest or lowest point — the maximum or minimum value. Axis of symmetry: a vertical line through the vertex that splits the parabola into mirror images. Intercepts: the y -intercept is where the graph crosses the y -axis; the x -intercepts (zeros/roots) are where it crosses the x -axis. Core Concept Forms of Quadratic Equations Standard form: y = ax^2 + bx + c , where a sets the direction and width of the opening. Vertex form: y = a(x - h)^2 + k , where (h, k) is the vertex. Factored form: y = a(x - r)(x - s) , where r and s are the x -intercepts (zeros). Converting: completing the square turns standard form into vertex form. Core Concept Three Solving Methods

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