Question

Describe the graph of the function. y = 9x2 + 18x – 6

Answer 1

The graph of the function y = 9x^2 + 18x - 6 is a parabola facing up with vertex at (-1, -5), x-intercepts at (-2.29, 0) and (0.29, 0) and y-intercept at (0, -4).

Answer 2

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)