What is the axis of symmetry and vertex for the graph # y=x^2 + 3x - 4#?
The vertex is
There are a couple ways to find the vertex - using
Method 1 (probably better method):
The equation is in standard quadratic form, or
To find the x-coordinate of the vertex in standard form, we use
Now, to find the y-coordinate of the vertex, we plug in our x-coordinate of the vertex back into the equation:
So our vertex is
If you think about it, the axis of symmetry is the line of the x-coordinate because that is where there is a 'reflection' or where it becomes symmetrical.
So this means that the line of symmetry is
Method 2: Converting into vertex form
We can also convert this equation into vertex form by factoring. We know that the equation is
To factor this, we need to find 2 numbers that multiply up to -4 AND add up to 3.
So it's factored into
Now our equation is
First, we need to find the x-intercepts (what x is when y = 0). To do this, let's set:
To find the x-coordinate of the vertex, we find the average of the 2 x-intercepts. Average is
(As you can see, it brings the same result as in
To find the y-coordinate of the vertex, we would pluck the x-coordinate of the vertex back into the equation and solve for y, just like we did in method 1.
You can watch this video if you still need help solving these: http://virtualnerd.com/algebra-1/quadratic-equations-functions/graphing/graph-basics/vertex-example
Hope this helps (sorry that it's so long)!