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3 years ago

Find the vertex of the parabola whose equation is y = x^2 + 8x + 12.

2 answers:

4 0

The vertex of a parabola is the point where the parabola crosses its axis of symmetry. If the coefficient of the x 2 term is positive, the vertex will be the lowest point on the graph, the point at the bottom of the “ U ”-shape.

The vertex of the parabola whose equation is y = x^2 + 8 x + 12 will be :
(x , y) = (-4,-4)

Black_prince [1.1K]3 years ago

3 0

Answer:

The vertex of the parabola is (-4,-4).

Step-by-step explanation:

If a quadratic function is defined as

$y=ax^2+bx+c$ ... (1)

Then the vertex of the function is

$Vertex=(\frac{-b}{2a},f(\frac{-b}{2a}))$

The given function is

$y=x^2+8x+12$ .... (2)

From (1) and (2), we get a=1,b=8 and c=12.

$\frac{-b}{2a}=\frac{-8}{2(1)}=-4$

Substitute x=-4 in the given equation.

$f(\frac{-b}{2a})=f(-4)=y=(-4)^2+8(-4)+12$

$y=16-32+12=-4$

Therefore the vertex of the parabola is (-4,-4).

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How to get the answer.

Anna007 [38]

9514 1404 393

Answer:

1.05 × 1.05 × 1.05 × 1.05 × 1.05 = 1.2762815625

Step-by-step explanation:

An exponent indicates how many times the base is a factor in the product. That is, 1.05 to the 5th power means ...

1.05⁵ = 1.05 × 1.05 × 1.05 × 1.05 × 1.05

This multiplication expression is evaluated in the usual way.

= 1.1025 × 1.05 × 1.05 × 1.05

= 1.157625 × 1.05 × 1.05

= 1.21550625 × 1.05

= 1.2762815625

All scientific and graphing calculators have a button for computing the power of a number. On my calculator its label is $\displaystyle \boxed{y^x}$ . The particulars of the function of this button can be found in the manual for your calculator.

For on-line calculators, such as the go.ogle calculator, or the Desmos graphing calculator, the caret (^) is used to signify an exponent. (See the input line in the first attachment for an example.)

6 0

3 years ago

If anyone Answer this question with POLITICALLY CORRECT answer I'll give you 25+ Points

Tresset [83]

Answer:

$\sqrt[4]{x^5}$

Step-by-step explanation:

A fraction exponent converts into a radical. The denominator is the index of the radical (farthest left number) and the numerator is the exponent of the base inside (the farthest right number). The base of the fraction exponent is the base number in green. To write this expression, simply the exponents into one exponent and one base.

$x^{\frac{3}{4}}x^{\frac{1}{2} } =x^{\frac{3}{4}}x^{\frac{2}{4} } =x^{\frac{3+2}{4}} =x^{\frac{5}{4}}$

Now convert to the radical.

$x^{\frac{5}{4}} = \sqrt[4]{x^5}$

8 0

3 years ago

Order the number from least to greatest 1/3,0.3,2/3 and 2/5

sammy [17]

0.3, 1/3, 2/5, 2/3
Hope this helps!

note: Do me a favor and mark me as brainliest? Would really help motivate me to help out more people. Thank you.

3 0

3 years ago

A rescue helicopter flew from its home base for 35 kilometers on a course of 330 degrees to pick up an accident victim. It then

artcher [175]

I've drawn a triangle to represent the journey (see attached.

The angle from Home to Victim to Hospital is:

a = $90 - (360 - 330) = 90- 30 = 60^o$

Using the cos rule, we can solve for the length x:

$a^2 = b^2 +c^2 - 2bccosA
\\x^2 = 35^2+25^2-2(35)(25)cos60
\\x^2 = 1850 - 875
\\x^2 = 975
\\x = \sqrt{975}
\\x = 31.2249...$

Using the cos rule, we can solve for angle b:

$a^2 = b^2 +c^2 - 2bccosA
\\35^2 = 31.22...^2+25^2-2(31.22...)(25)cosb
\\1225 = 975 + 625 - 1561.249...cosb
\\-375 = -1561.249...cosb
\\b = cos^{-1}( \frac{-375}{-1561.249...}) 
\\b = 76.1...$

So the bearing the helicopter has to travel is:

270 - 76.1 = 193.9 degrees (1 dp)

And the distance it travels is 31.2 km (1 dp)

5 0

3 years ago

Is 5xy and -8xy similiar explain why

user100 [1]

The given algebraic expressions 5xy and -8xy are like terms because of the similarity in their variable and it's power.

As per the question statement, we are given algebraic expressions 5xy and -8xy and we are supposed to tell whether these two terms are like or not.

We know that in Algebra, the phrases or terms that include the same variable and are raised to the same power are referred to as "like terms."

Hence as the variable part in the expressions, 5xy and -8xy, are same hence they can be added and subtracted hence are called like terms.

Algebraic expressions: An expression which is constructed using integer constants, variables, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)
Like terms: The definition of similar words is the terms that have the same variable raised to the same power. Only the numerical coefficients can alter in terms that are similar to algebra. We may combine similar words to make algebraic expressions simpler, making it much simpler to determine the expression's outcome.

To learn more about algebra, click on the link given below:

brainly.com/question/24875240

#SPJ1

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1 year ago