Expert: Sherry Wallin - 12/27/2009

Question
Draw the graph of the function y = 2x2 + 3x – 3 between x = -6 and x = 5. By observation, where does this curve cross the x axis? Try to confirm this by substitution in the equation.

Answer
Sam I assume you mean y = 2x^2 + 3x - 3. Set y = 0 which means you need to factor 2x^2+3x-3 = 0 ->
you will need to use the quadratic equation to find where the graph crosses the x-axis. You could make a table of values between -6 and 5 and see what the parabola looks like. I can tell you this parabola opens up and that it crosses the x axis twice and where this happens is where y = 0.
x = [-3 +- sqrt(3^2-4(2)(-3))]/2(2) = [-3+-sqrt(20)]/4 = [-3+-2sqrt5]/4 -> x = [-3+2sqrt5]/4 and
[-3-2sqrt5]/4 which is approximately .37 and -1.87

Math Prof