Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 9 - Section 9.5 - Graphs of Quadratic Equations - Exercise Set: 19

Answer

$(2,-1)$

Work Step by Step

Completing the square of the right side of the given equation, $ y=x^2-4x+3 ,$ results to \begin{array}{l}\require{cancel} y=(x^2-4x)+3 \\\\ y=\left( x^2-4x+\left( \dfrac{-4}{2} \right)^2 \right)+3-\left( \dfrac{-4}{2} \right)^2 \\\\ y=\left( x^2-4x+\left( -2 \right)^2 \right)+3-\left( -2 \right)^2 \\\\ y=\left( x^2-4x+4 \right)+3-4 \\\\ y=\left( x-2 \right)^2-1 .\end{array} The vertex of the parabola whose quadratic equation is in the form $y=a(x-h)^2+k$ is $(h,k)$. Hence, the vertex of the equation above is \begin{array}{l}\require{cancel} (2,-1) .\end{array}
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