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Anika [276]
1 year ago
14

Find the vertex and the axis of symmetry for the following functions.

Mathematics
2 answers:
bearhunter [10]1 year ago
7 0

Answer:

b

Step-by-step explanation:

its correct

Xelga [282]1 year ago
4 0

Step-by-step explanation:

a)

y = 2x³ + 4x

a polynomial of 3rd degree cannot have an axis of symmetry.

it can only have a point of symmetry, like in this case.

(0, 0) is the point of symmetry, because due to the fact there is no squared term, any negative x values create exactly the same values (in absolute values) as their positive counterparts - just negative.

the vertex of a polynomial of 3rd degree is the point where the function changes directions.

that point for x³ is the origin, as it is for x. the factors only stretch the graph, but the vertex stays the same.

only if we had a term like (x+a)³ in the polynomial, this would shift the vertex.

so, the point of symmetry and the vertex are the same :

(0, 0).

b)

y = -x² + 4x - 5

the vertex form of a quadratic function is

f(x) = a(x − h)² + k

with (h, k) is the vertex.

x = h is the axis of symmetry.

we use "complete the square" to get it into that form.

-x² + 4x - 5 = -(x² - 4x + 5) = -(x - 2)² - 1

therefore,

y = -(x - 2)² - 1

h = 2, k = -1

the vertex is (2, -1)

the axis of symmetry is x = 2

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(5x+2) and {3(x+14)} what is
Phoenix [80]

Answer:

Step-by-step explanation:

x=20

Reorder the terms:

(2 + 5x) = 3(x + 14)

Remove parenthesis around (2 + 5x)

2 + 5x = 3(x + 14)

Reorder the terms:

2 + 5x = 3(14 + x)

2 + 5x = (14 * 3 + x * 3)

2 + 5x = (42 + 3x)

Solving

2 + 5x = 42 + 3x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3x' to each side of the equation.

2 + 5x + -3x = 42 + 3x + -3x

Combine like terms: 5x + -3x = 2x

2 + 2x = 42 + 3x + -3x

Combine like terms: 3x + -3x = 0

2 + 2x = 42 + 0

2 + 2x = 42

Add '-2' to each side of the equation.

2 + -2 + 2x = 42 + -2

Combine like terms: 2 + -2 = 0

0 + 2x = 42 + -2

2x = 42 + -2

Combine like terms: 42 + -2 = 40

2x = 40

Divide each side by '2'.

x = 20

Simplifying

x = 20

7 0
3 years ago
What is the length of the altitude of the equilateral triangle below?​
ElenaW [278]

Answer:

A

Step-by-step explanation:

the height a creates with half of the baseline (5) and a leg (10) a right-angled triangle, and we can use Pythagoras to calculate a.

c² = a² + b²

c being the Hypotenuse (the side opposite of the 90° angle, so in our case the 10 side).

10² = a² + 5²

100 = a² + 25

75 = a²

a = sqrt(75) = sqrt(3×25) = 5×sqrt(3)

5 0
2 years ago
What is 2/6 simplified?
m_a_m_a [10]
1/3 is the answer. Hope this helps
3 0
3 years ago
Write the sentence as an equation.<br> c is 256 subtracted from g
romanna [79]

Answer:

c = g - 256

Step-by-step explanation:

The word "is" indicates an equal sign, and saying you take 256 from g is g - 256.

3 0
3 years ago
Dimension of a cuboid is 4 m 3 m ad 5 m how many such cuboid can form a cube....... please and urgent..experts please help
larisa [96]

Step-by-step explanation:

We dimension of the smallest cube to be made from cuboids of sides 3 m , 4 m and 5 m will be the least common multiple of 3 m, 4 m and 5 m i.e. 60 m

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hope it helps

4 0
3 years ago
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