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Fantom [35]
3 years ago
9

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

Mathematics
2 answers:
Vika [28.1K]3 years ago
5 0
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).
Lina20 [59]3 years ago
4 0

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 <u>+</u> √Δ /2a = -18 <u>+</u> 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)

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Step-by-step explanation:

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In the given graph point B is a relative maximum with the coordinates (0, 2).

The given function is y=x^{4}-2x^{2} +1.

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The function's graph makes it simple to spot relative maxima. It is the pivotal point in the function's graph. Relative maxima are locations where the function's graph shifts from increasing to decreasing. A point called Relative Maximum is higher than the points to its left and to its right.

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