You could have made a sketch of this equation in about 5 minutes and figured out where the vertex is located.Sarah Kenney said:Homework Statement
I'm trying to find the vertex of this parabola: y^2-12=12x
The Attempt at a Solution
Initially I tried to take the derivative and find the vertex by finding where it the function is zero, but apparently that does not work in this situation. Is it because it is not in standard form? I've been staring at this problem for hours. I need a hint.
Thanks.
In future posts, please show what you have tried, rather than describe it.Sarah Kenney said:Ok, so I figured it out.
It's:
y^2=12x+12
y^2=12(x+1)
x=-1
So y= 0
I don't know why that took me so long. Math brain.
Thanks.
The vertex of a parabola is the point where the parabola changes direction. It is the highest or lowest point on the parabola, depending on whether the parabola opens upward or downward.
To find the vertex of a parabola from the given equation, we can use the formula h = -b/2a, where a and b are the coefficients of the x^2 and x terms, respectively. In the equation y^2-12=12x, a=12 and b=0. Therefore, the vertex is (0,0).
The y^2-12=12x solution represents the set of points that satisfy the equation and form a parabola. It is the graph of a parabola with a vertex at (0,0) and a focus at (6,0).
To graph the parabola, you can plot the vertex, which is (0,0), and two other points on the parabola. These points can be found by substituting different values for x into the equation. Then, connect the points to form a smooth curve.
Yes, the vertex of a parabola can be located at a negative point. In fact, the vertex can be located at any point on the coordinate plane, depending on the equation of the parabola.