# Finding the equation of a parabola from its graph [closed]

can chat on discord but need help asap really struguling in this class

• Welcome to Math.SE. We want to help learners of math at all levels, but you are required to research your problem before asking. See the site tour and the part of the FAQ about how to ask. May 18 at 23:21
• For multiple choice like this, it is easy enough to pick two points you know are on the curve and check to see if they fit the desired equations. For instance, $(2,1)$ and $(6,5)$ should both be on the curve. May 18 at 23:21
• I notice the vertex and notice it's open to the right. Only one choice satisfies that. May 18 at 23:25

From the graph, we know that the vertex of the parabola is (2, 1). So, plugging in $$x=2$$ and $$y=1$$, only the last two equations are plausible (like JMoravitz said). Now, from the last two, $$x$$ is always greater than or equal to $$2$$ on the entire parabola, and any real number squared is always positive, so $$(y-1)^2>0$$. Thus, it cannot be $$-1/4$$ times $$(y-1)^2$$, because the left-hand side must end up positive, because $$x-2$$ always is (like randomgirl said). So, the correct answer is the fourth choice.
The parabola opens to the right, and its vertex is at $$(2, 1)$$
$$x - 2 = K (y - 1)^2$$ where $$K \gt 0$$
Only one choice satisfies this, which is the choice $$(D)$$.