SOLUTION: if y=2x(squared)+6x+1 what are the coeffecients, what is the vertex of the parabola, what is the axis of symmetry, what is the y-intercept, and if it is reflected across the y-inte

Question 166890: if y=2x(squared)+6x+1 what are the coeffecients, what is the vertex of the parabola, what is the axis of symmetry, what is the y-intercept, and if it is reflected across the y-intercept across the axis of symmetry x=_____, x=______

pleas help i'm in jeapordy of failing. contact me- for subject put alg 2
o and we do nnot use a textbook to do work.
Answer by MRperkins(300) (Show Source): You can put this solution on YOUR website!
Here are some book definitions for you:
A MONOMIAL is a real number, a variable, or a product of real numbers adn variables. The expressions -15, 3z and are all monomials.
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The COEFFICIENT of a monomial is its numerical factor. For example, the coefficient in is -2.8.
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The DEGREE OF A MONOMIAL is the sum of the exponents of the monomial's variables. The degree of is 11 because 7+3+1=11.
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A POLYNOMIAL is an expression that is either a monomial or a sum or difference of monomials. Each monomial component of a polynomial is called a TERM. The terms of a polynomail are usually arranged in descending order of powers.
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The LEADING COEFFICIENT of a polynomial is the coefficient of the first term when the polynomial is written in descentding order of powers. For example, the leading coefficient of is -1.
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The DEGREE OF A POLYNOMIAL is equal to the greatest of the degrees of the polynomial's terms. Polynomials are classified by their degree and by thier number of terms. The polynomial is classified as a cubic(degree-three) trinomial. The polynomial is an example of a quadratic (degree-two) binomial.
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I know this may sound like a lot but it is only 6 or 7 definitions and if you understand these definitions then all of this will be much easier to understand.
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the coefficients are simply the number(1,2,3...) in front of a variable(a,b,x,y,...)
so the coefficients in this problem are 2,6, and 1.
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In order to find the vertex of the parabola we need to put the equation in vertex form.
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VERTEX FORM:
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By using a process called COMPLETING THE SQUARE, we can rewrite a quadratic function of the form in the form
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Write your problem in VERTEX FORM.
We want to rewrite the quadratic expression so that it contains a trinomial of the form --the square of a binomial x+a. To do so, WE ADD TO THE FIRST TWO TERMS THE SQUARE OF HALF THE LINEAR COEFFICIENT. THEN, SO THAT WE DO NOT CHANGE THE VALUE OF THE EXPRESSION, WE MUST SUBTRACT THE SAME VALUE.
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Factor out the 2. (the leading coefficient must always be 1 for the complete the square method to work)
rewrite, leaving space to add and subtract a quantitiy. f(x)=2(x^2+3x+___)-____+1
Complete the square by adding and subtracting (1/2 *3)^2. Because we had to factor out the two, we need to multiply (9/4) by 2 in order to keep the equation equal (this part is tough to explain in writing so if you do not understand it then email me and I will call you): f(x)=2(x^2+3x+(9/4))-2(9/4)+1
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Factor the perfect-square trinomial and add the constants or
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The vertex is going to be the value of x when (x+(3/2))=0
so the vertex is x=(-3/2).
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It is reflected across the line x=-3/2 and intersects the x-axis at

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I hope this helps!
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Private tutoring is available. Click on my name to go to my website or email me at justin.sheppard.tech@hotmail.com for more information. If you have any other questions you can direct them to me personally and I will answer them for you.

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