Converting to Vertex Form by Completing the Square

Algebra 2 · Axiom Academy

EXAMPLE Converting to Vertex Form by Completing the Square Transform y = 2x^2 - 8x + 3 into vertex form to find the parabola's vertex. Convert y = 2x^2 - 8x + 3 into vertex form, y = a(x-h)^2 + k , by completing the square, and identify the vertex (h, k) . Nice work — you converted a quadratic from standard form into vertex form by completing the square. The pieces worth keeping: Factor first (if ): pull the leading coefficient out of the x^2 and x terms before completing the square — y=2x^2-8x+3 becomes y=2(x^2-4x)+3 . Complete the square with (b/2)^2 : here b=-4 (the coefficient INSIDE the parentheses), so (b/2)^2=(-4/2)^2=4 . Carry the leading coefficient through the compensation term: subtracting 4 inside parentheses multiplied by 2 is really subtracting once distributed — dropping that factor is the most common mistake in this topic. Vertex form is y=a(x-h)^2+k : the vertex is (h,k) . Read the vertex directly: y=2(x-2)^2-5 gives vertex (2,-5) — opposite sign for h (from x-2 ), same sign for k . Since , the parabola opens upward. This factor–complete–simplify routine works for any quadratic, no matter the size of the leading coefficient — practice it on a few more to make it automatic.

This is the written version of the interactive lesson above. See the full Algebra 2 course.