Using the Discriminant, D=b^2 - 4ac, determine the number of x-intercepts the expression below has.

Question

Using the Discriminant, D=b^2 - 4ac, determine the number of x-intercepts the expression below has.

-2(x+3)^2 - 20 = 0

a=....... b= ........ c=...........

Answer 1

First thing you need to do is to convert this to standard form

-2(x^2+6x+9) -20

-2x^2 -12x- 18 -20 = -2x^2 -12x-38 so a = -2 b= -12 and c=-38

b^2-4ac = (-12)^2 -4(-2)(-38) = 144- -304 = -160 Since the discriminate is negative there are no real solutions and the graph does not cross the x axis

You could have figured this out by examining the equation in vertex form

The vertex is at (-3,-20) which is below the x axis and the leading coefficient of the x^2 term is negative so the parabola is downward facing so the y values continue to decrease which means the expression will never cross the x axis