SOLUTION: Help I am so confused. 1) 2x^2=6 what are the solutions x= what are the x intercepts 2) 10T^2-8T = 0 What is the nature of the solution 3) what is the ve

Algebra.Com
Question 194985: Help I am so confused.
1) 2x^2=6 what are the solutions x=
what are the x intercepts
2) 10T^2-8T = 0 What is the nature of the solution
3) what is the vertex of f(x)=-x^2+12x+3

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Help I am so confused.
1) 2x^2=6 what are the solutions x=
what are the x intercepts
The x-intercepts are the solutions.
2x^2 = 6
x^2 = 3
x = ± sqrt(3)
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=12 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 1.73205080756888, -1.73205080756888. Here's your graph:

---------------------
Ignore the factoring statement.
-------------------
2) 10T^2-8T = 0 What is the nature of the solution
It's a parabola with the vertex (maximum) at the top (assuming T is horizontal).
----------------
3) what is the vertex of f(x)=-x^2+12x+3
The vertex is at x = -b/2a
or x = -12/(12) = 6
At x = 6, f(x) = -36 + 72 + 3 = 39
--> (-6,39)

RELATED QUESTIONS

I am confused as to how i would work this out. Please help? *Determine the nature of the (answered by sudhanshu_kmr)
Determine the nature of the solutions of the equation 10t^2 - 8t = 0. 2) give exact and... (answered by ewatrrr)
7x+x(x-2)=0 what are the solutions? What are the... (answered by ewatrrr)
A.) Solve 6x+x(x-2)=0 What are the solutions? B.) find the x-intercepts of... (answered by checkley77)
a)SOLVE 2X^2=6 b) Find the x-intercepts of f(x)=2x^2-6 What are the solutions?... (answered by jim_thompson5910)
Sketch the graph of f(x) = 2x^2 (x-1)^3 (x+2) I know that the X intercepts are 1, -2, and (answered by lwsshak3)
a.) solve 2x^2=10 What are the solutions? b.) find the x-intercepts of f(x)=2x^2-10... (answered by jrfrunner)
f(x)=1/2x^2+6x+7 I know that the vertex is (-6,-11) I know that the graph opens up. (answered by stanbon)
Determain the nature of the solutions. x^2+18=0 A. 1 real solution B. 2 imaginary... (answered by jim_thompson5910)