The vertex of the parabola defined by the equation y² - 12 = 12x is located at the point (-1, 0). The initial approach of using derivatives to find the vertex was ineffective due to the equation not being in standard form. The correct method involves rewriting the equation as y² = 12(x + 1), which clearly indicates the vertex's coordinates. This solution emphasizes the importance of recognizing the form of the equation when determining the vertex of a parabola.
PREREQUISITESStudents studying algebra and calculus, educators teaching conic sections, and anyone seeking to understand the properties of parabolas.
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.