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

Algebra/Trig Review3.2y x x=− + 2 + 3SolutionThis is also the graph of a parabola only it is in the more general form.2y = ax + bx + cbIn this form, the x-coordinate of the vertex is x = − and we get the y-coordinate by2aplugging this value back into the equation. So, for our parabola the coordinates of thevertex will be.2x =− = 12 −1( )2( ) ( )y =− 1 + 21+ 3=4So, the vertex for this parabola is (1,4).We can also determine which direction the parabola opens from the sign of a. If a ispositive the parabola opens up and if a is negative the parabola opens down. In ourcase the parabola opens down.This also means that we’ll have x-intercepts on this graph. So, we’ll solve thefollowing.2− x + 2x+ 3=02x −2x− 3=0( x− 3)( x+ 1)= 0So, we will have x-intercepts at x = − 1 and x = 3. Notice that to make my life easier2in the solution process I multiplied everything by -1 to get the coefficient of the xpositive. This made the factoring easier.Here’s a sketch of this parabola.© 2006 Paul Dawkins 22http://tutorial.math.lamar.edu/terms.aspx