Question

Graph the function. y = 2x^2 + 4x

Answer 1

Answer:

Step-by-step explanation:

The function y = 2x^2 + 4x has a parabolic graph that opens up.  

*In factored form we have y = 2x(x + 2); if we set this equal to zero and solve for x, we obtain {-2, 0}, the roots of this function.  

*The axis of symmetry is halfway between these roots:  x = -1.  The y-value of the vertex is the value of the function at x = -1:  f(-1) = 2(-1)^2 + 4(-2) = -6.  Thus, the vertex is (-1, -6).

* The y-intercept is (0, 0), since y = 0 when x = 0.

Graph the points shown and draw a smooth curve through them, remembering that this parabola opens up.