Problema Solution
Graph y=2x2(squared)+6x-40 on an appropriate set of axes. Adjust the minimum value on the y-axis so that the vertex can be seen in the viewing window. Find the x-interceplts, y-intercept,and relative maximum or relative minimum.
Answer provided by our tutors
the x-intercepts are when y = 0
y = 2x2 + 6x - 40
0 = 2x2 + 6x - 40
x = -3 +/- sqrt(89) / 2
so ((-3+sqrt(89))/2,0) and ((-3-sqrt(89))/2,0) are the x-intercepts
y-intercept is when x = 0
y = 2(0)2 + 6(0) - 40
y = -40
so (0,-40) is the y-intercept
vertex:
x = -b/2a
x = -6/4
x = -3/2
y = 2(-3/2)2 + 6(-3/2) - 40
y = -187/4 = -46.75
(-3/2,-187/4) is the vertex and it is a minimum since the coefficient of the squared term is positive & the parabola opens up