What is the equation of the axis of symmetry of the graph of y + 3x 6 =

What is the equation of the axis of symmetry of the graph of y + 3x – 6 = –3(x – 2)squared + 4?

2 months ago

Solution 1

Guest Guest #4117
2 months ago


x = 3/2

Step-by-step explanation:

That is quite long and drawn out, so we have to get it down to a single quadratic equation, set equal to 0.

Begin by expanding the right side to get


then multiplying in the -3 to get


Now we will combine all the like terms and get everything on one side of the equals sign, and set it equal to 0:


In order to find the equation of the axis of symmetry we have to put it into vertex form, which is accomplished by completing the square on this quadratic.

In order to complete the square, the leading coefficient has to be a +1.  Ours is a -3, so we will factor that out.  First, though, now that it is set to equal 0, we will move the constant, -2, over to the other side, isolating the x terms.


Now we can factor out the -3:


The rules for completing the square are as follows:

Take half the linear term, square it, and add it to both sides.  Our linear term is 3.  Half of 3 is 3/2, and squaring that gives you 9/4.  We add into the parenthesis on the left a 9/4, but don't forget about that -3 hanging around out front that refuses to be ignored.  We didn't add in just a 9/4, we added in (-3)(9/4) = -27/4:


In the process of completing the square we created a perfect square binomial on the left.  Stating that binomial and simplifying the addition on the right gives us:


We can determine the axis of symmetry at this point.  Because this is a positive x-squared polynomial, the axis of symmetry is in the form of (x = ) and what it equals is the h coordinate of the vertex.  Our h coordinate is 3/2; therefore, the axis of symmetry has the equation x = 3/2

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Step-by-step explanation:

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Solution 1


Inequality to find the age of siblings is x²+ 11x + 24 ≤ 150.

Step-by-step explanation:

Let the age of Holly is x years. Now from the statements of the question we will form the equations.

Sue was born three years before Holly.

Sue = Holly + 3 = x + 3------(1)

Jeremy = Sue + 5

From equation (1)

Jeremy = (x + 3) + 5 = x + 8------(2)

Now statement says the product of Sue's age and Jeremy's age is at most 150.

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x² + 11x + 24 ≤ 150

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Solution 2

Answer: x^2+11x+24 </= 150

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Regression equation: y = 3.915(1.106)x the pond can hold 400 water lilies. by what day will the pond be full? write and solve an equation. the pond will be full by the end of day
Solution 1


46 days

Step-by-step explanation:

Given : Regression equation: y = 3.915(1.106)^x


 y = amount of water lilies the pond hold

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Solution 2
46 Days

It said I have to have at least 20 characters to explain it well so here.
I hope you have a good day
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Solution 1

The improper fraction will be  - 34/3

Mixed fractions are expressed as a \frac{b}{c}, expressing as an improper fraction will give:

a\frac{b}{c}  = \frac{(a\times c) + b}{c}

Given the mixed fraction -11\frac{1}{3}, applying the formula above to express as an improper fraction will give:

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Learn more here: brainly.com/question/24901550

Solution 2

-11 1/3 = -34/3 put the