Which of the following equations is of a parabola with a vertex at (0, 3)? y = (x - 3) 2

Question

Which of the following equations is of a parabola with a vertex at (0, 3)?

y = (x - 3) ²

Answer 1

NO! y=(x-3)^2 is not correct!!! when x=0, y = 9 !!!!

vertex happens at -b/2a...... SO,

-b/2a = 0 which forces b = 0

the quadratic function is then ax^2 + c

f(0) = 3 ---> when x=0, c = 3

the function is now:

f(x) = ax^2 + 3

Your function looks something like that

Answer 2

While there do need to be more options (since the one given is not correct) we can still come up with the right answer.

The general equation for a parabola for a given vertex at (a,b) is y=(x-a)^2+b. Since you want the vertex to be at (0,3) we know the equation will be:

y=(x-0)^2+3=x^2+3

Hope this helps!

Answer 3

Basic parabola:

y = x²

If the vertex is at (0,3), it means the curve is shifted 3 units up. This means that y gets replaced by y-3.

So the equation is y - 3 = x²

^OR:

y = x² + 3

To help understand these things, plot the curves on a graph---if necessary, use one of the online tools such as DESMOS:

https://www.desmos.com/calculator