# 6x²-12x-25=-7 vertex axis of symmetry

Mathematics

2 answers:

3241004551 [841]2 years ago

6 0

Answer:

Step-by-step explanation:

-b

The axis of symmetry can be calculated using this formula: x = ------

-(-12)

which in this case is x = ---------- = 1. The axis of symmetry is the vertical

2(6) line x = +1

Thus, x = 1 is the x-coordinate of the vertex. Normally we'd find the y-coordinate by evaluating the function at x = 1. Unfortunately your

6x²-12x-25=-7 does not have the form of a quadratic function; such a function does not have the " = " sign in it.

Example: Suppose we have 6x²-12x-25 = f(x) and we evaluate this function at x = 1: f(1) = 6(1)^2 - 12(1) - 25 = -31, which (in this example)

leads to the vertex (1, -31).

tino4ka555 [31]2 years ago

4 0

Axis of symmetry: x=1
Vertex: (1, -24)

Explanation:

6x²-12x-25=-7

6x²-12x-18=0

a=6, b=-12, c=-18

Formula of axis of symmetry: x=-b/2a

x=-b/2a

x= -(-12)/2(6)

x= 12/12

x= 1

Vertex: (1,?)

Sub x= 1 into the equation,
6(1)² - 12(1) - 18 = y

6 - 12 - 18 = y

y = -24

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For the function y=-1+6 cos(2pi/7(x-5)) what is the minimum value?

Ad libitum [116K]

Usually one will differentiate the function to find the minimum/maximum point, but in this case differentiating yields:
$\frac{2\pi}{7(x-5)^{2}}\sin{\frac{2\pi}{7(x-5)}}}$
which contains multiple solution if one tries to solve for x when the differentiated form is 0.

I would, though, venture a guess that the minimum value would be (approaching) 5, since the function would be undefined in the vicinity.

If, however, the function is
$-1+\cos{\frac{2\pi}{7}(x-5)}}$
Then differentiating and equating to 0 yields:
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which gives:
$x=5$ or $8.5$

We reject x=5 as it is when it ix the maximum and thus,
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