Question

Write the equation of the parabola in vertex form vertex (0,0) passes through (2,1)

Answer 1

Answer:

$f(x)=\frac{1}{4}x^2$

Step-by-step explanation:

Recall the vertex form of a quadratic equation:

$f(x)=a(x-h)^2+k$

Where (h,k) is the vertex.

We are told that the vertex is (0,0). Therefore:

$f(x)=a(x-0)^2+(0)$

Simplify:

$f(x)=ax^2$

So, to finish the equation, we need to find a.

We know that a point is (2,1). Thus, substitute 1 for f(x) and 2 for x:

$1=a(2)^2$

Square:

$1=4a$

Divide both sides by 4:

$a=\frac{1}{4}$

So, our a value is 1/4.

And we can thus complete our equation:

$f(x)=\frac{1}{4}x^2$

And we are done :)