Graphing Functions

Question

Estimate the following:

The roots of the function y=2x²+2x-4

 

The solutions of the equation 2x²+2x-4=-3

 

Answer 1

2x^2 + 2x -4

= 2(x^2 +x ) -4

=2(x^2 + x + 1/4) - 4 -1/2

= 2(x+ 1/2)^2 - 9/2

is a an upward opening parabola with vertex (-1/2, -9/2) = minimum point

axis of symmetry is x= -1/2

y intercept is -4 or (0,-4)

roots are the x intercepts found by setting y=0

2x^2 +2x -4 = 0

x^2 +x -2 = 0

x^2 + x + 1/4 = 2+1/4

(x+1/2)^2 = 9/4

x +1/2 = + or - 3/2

x = -1/2 + or - 3/2 = 2 or -1

x=-1 and x =2 are the two roots

using Descartes' rule of signs, you know there was 1 real positive root and 1 real negative root maximum

or a conjugate pair of imaginary roots.