Question

Determine in which direction the parabola below opens. y = 8x2 - 3x - 9

Answer 1

y = ax^2 + bx + c

If a > 0, the parabola opens upwards <=
If a < 0, it opens downwards

y = 8x^2-3x-9
y+9 = 8x^2-3x
y+9 = 8(x^2 -3/8 x)
y+9 = 8( x^2 - (2)(3/8)(1/2) x + (3/16)^2 -(3/16)^2 )
y+9 = 8(x-3/16)^2 - 8(3/16)^2
y+9 = 8(x-3/16)^2 -72/256
y = 8(x-3/16)^2 -9 -72/256
y= 8(x-3/16)^2 -297/32

Vertex : (3/16, -297/32)

Answer 2

The parabola opens upward. because 8x^2 is positive