SOLUTION: Find the axis of symmetry. y = x^2 – x – 8 My answer that I got is x=1 Is that correct?

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Question 84352: Find the axis of symmetry.
y = x^2 – x – 8
My answer that I got is x=1
Is that correct?
Found 3 solutions by tutor_paul, bucky, Edwin McCravy:
Answer by tutor_paul(519) About Me  (Show Source):
You can put this solution on YOUR website!
You find the axis of symmetry from:
x=-b%2F2a
x=-%28-1%29%2F2
highlight%28x=1%2F2%29
=========================
See the graph below:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-1x%2B-8+=+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=%28-1%29%5E2-4%2A1%2A-8=33.

Discriminant d=33 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+33+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+33+%29%29%2F2%5C1+=+3.37228132326901
x%5B2%5D+=+%28-%28-1%29-sqrt%28+33+%29%29%2F2%5C1+=+-2.37228132326901

Quadratic expression 1x%5E2%2B-1x%2B-8 can be factored:
1x%5E2%2B-1x%2B-8+=+1%28x-3.37228132326901%29%2A%28x--2.37228132326901%29
Again, the answer is: 3.37228132326901, -2.37228132326901. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1%2Ax%2B-8+%29

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
There are several ways that you can find the value of x that represents the axis of symmetry.
.
One of these ways is to get the quadratic equation in the form that you need to apply the
quadratic formula. That form is:
.
ax%5E2+%2B+bx+%2B+c
.
Then recognize that the axis of symmetry is determined by that term of the of the answer to
the quadratic equation that is:
.
-b%2F%282%2Aa%29
.
In this case, by comparing the quadratic expression of the problem:
.
x%5E2-x-8
.
with the standard quadratic form:
.
ax%5E2+%2B+bx+%2B+c
.
you can see that a = 1, b = -1, and c = -8. Substitute the appropriate values here into:
.
-b%2F%282%2Aa%29
.
and you get:
.
-%28-1%29%2F%282%2A1%29+=+1%2F2+
.
So the answer to this problem is that the equation for the line of symmetry is:
.
x+=+1%2F2
.
Hope that this clarifies the significance of the first term in the quadratic formula:
.
x+=+-b%2F2a+%2B-+%28sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
.
It is the axis of symmetry about which the answers are equally spaced in both the + and
the - directions.
.

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Find the axis of symmetry.
y = x² – x – 8 
My answer that I got is x=1
Is that correct?

No. the equation of the axis of symmetry of

y = ax² + bx + c 

is the vertical line whose equation is

x = -b%2F2a

In your problem, whixch is the same as

y = 1x² - 1x - 8

a = 1, b = -1 and c = -8

x = %28-%28-1%29%29%2F2%281%29

x = 1%2F2

Edwin