Algebra/Trig Review - Pauls Online Math Notes - Lamar University

Algebra/Trig Review2. ( ) 2y = x+ 3 − 1SolutionThis is a parabola in the formy = ( x− h) 2+ kParabolas in this form will have the vertex at (h, k). So, the vertex for our parabola is(-3,-1). We can also notice that this parabola will open up since the coefficient of thesquared term is positive (and of course it would open down if it was negative).In graphing parabolas it is also convenient to have the x-intercepts, if they exist. Inthis case they will exist since the vertex is below the x-axis and the parabola opensup. To find them all we need to do is solve.2x + 3 − 1=0( )( x )2+ 3 = 1x + 3=±1x=− 4 and x=−2With this information we can plot the main points and sketch in the parabola. Here isthe sketch.© 2006 Paul Dawkins 21http://tutorial.math.lamar.edu/terms.aspx