SOLUTION: Consider the equation with the formula y=x squared+6x-1 A)find the values of x when y=0 B) find the vertex of the parabola C) graph the parabola and d) give the line of symm

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Consider the equation with the formula y=x squared+6x-1 A)find the values of x when y=0 B) find the vertex of the parabola C) graph the parabola and d) give the line of symm      Log On


   

Question 25661: Consider the equation with the formula y=x squared+6x-1 A)find the values of x when y=0 B) find the vertex of the parabola C) graph the parabola and d) give the line of symmentry
I believe for part B i first must get the formula into vertex form and that should help me with the rest of the parts to the question but for part A, I do not understand how i would answer with the qaudratic Formula. Would it be -6 plus or minus the square root of 6 squared - 4*a*c over 2*a ?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
y=x^2+6x-1
A) Let y=0:
x^2+6x-1=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B6x%2B-1+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%286%29%5E2-4%2A1%2A-1=40.

Discriminant d=40 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+40+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%286%29%2Bsqrt%28+40+%29%29%2F2%5C1+=+0.16227766016838
x%5B2%5D+=+%28-%286%29-sqrt%28+40+%29%29%2F2%5C1+=+-6.16227766016838

Quadratic expression 1x%5E2%2B6x%2B-1 can be factored:
1x%5E2%2B6x%2B-1+=+1%28x-0.16227766016838%29%2A%28x--6.16227766016838%29
Again, the answer is: 0.16227766016838, -6.16227766016838. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B6%2Ax%2B-1+%29

B) Complete the square:
y= (x^2+6x+9)-1-9
y=(x+3)^2-10
y+10=(x+3)^2
This is in "vertex" form:
h=-3, k=-10
C) The axis of symmetry is x=-3
Cheers,
Stan H.