Problema Solution

Graph y=4x2(squared)-6x-2 on the standard axes. Find the x-intercepts, y-intercept, and vertex. Determine whether the vertex is a relative maximum or a relative minimum.

Answer provided by our tutors

the x-intercepts are when y = 0

y = 4x2 - 6x - 2

0 = 4x2 - 6x - 2

x = 3 +/- sqrt(17) / 4

so ((3+sqrt(17))/4,0) and ((3-sqrt(17))/4,0) are the x-intercepts

y-intercept is when x = 0

y = 4(0)2 - 6(0) - 2

y = -2

so (0,-2) is the y-intercept

vertex:

x = -b/2a

x = 6/8

x = 3/4

y = 4(3/4)2 - 6(3/4) - 2 

y = -17/4

(3/4,-17/4) is the vertex and it is a minimum since the coefficient of the squared term is positive & the parabola opens up