Graphing y = x² - 4x + 3

Algebra 1 · Axiom Academy

Graph y = x^2 - 4x + 3 by finding its vertex with the formula and using symmetry. Graph the quadratic function y = x^2 - 4x + 3 . Find the vertex using the formula , locate the intercepts, and use symmetry to sketch the parabola. Here is y = x^2 - 4x + 3 with every point we found — the red vertex, the blue intercepts and mirror point, and the green dashed axis of symmetry. Nice work — you graphed a quadratic from its standard form by locating the vertex and using symmetry. Remember: Vertex formula: for y = ax^2 + bx + c , the vertex sits at ; substitute back to get its y -value. Axis of symmetry: the vertical line — here x = 2 . Use symmetry: points the same distance left and right of the axis share a y -value, so each plotted point gives a free mirror point. x-intercepts: set y = 0 and solve. Here x^2 - 4x + 3 = (x-1)(x-3) = 0 gives (1, 0) and (3, 0) . Direction: since , the parabola opens upward and the vertex (2, -1) is its minimum. This same method graphs any quadratic in standard form: find the vertex, draw the axis, mirror the intercepts, and connect the points into a smooth parabola.

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