Answer: Roots: 0.3 and -2.3
y-intercetpt (0,-6)
vertex (-1,-15)
Step-by-step explanation: it's a parabola.
As a = 9 and it is > 0, it is facing up.
To find the roots:
9x² + 18x - 6 = 0
a = 9; b = 18; c = -6
Δ = b² - 4ac = 18² - 4.9.(-6)
Δ = 324 + 216 = 540
√Δ = √540 = 23.24
x = -b + √Δ /2a = -18 + 23.24/18
x₁ = -18 + 23.24/18 = 0.3
x₂ = -18 - 23.24/18 = -2.3
So, it intercepts x (0.3;0) and (-2.3;0)
For the y-intercept → x = 0
9.0² + 18.0 - 6 = -6
So, it intercepts y on (0,-6)
For the vertex
xv = -b/2a = -18/18 = -1
yv = -Δ/4a = -540/36 = -15
So, the vertex is (-1,-15)
