Question

If the vertex of a parabola is at (2, 3) and the point (0, -1) is also on the parabola, find an equation for the parabola. Write your answer in the form () = ( − ℎ)2 + .

Answer 1

Answer:

$y=-1(x-2)^2+3$

Step-by-step explanation:

W have been given that the vertex of a parabola is at (2, 3) and the point (0, -1) is also on the parabola. We are asked to find the equation of parabola in the form $y=(x-h)^2+k$.  

We know that vertex form of parabola in form $y=a(x-h)^2+k$, where (h,k) in vertex of parabola.  

Upon substituting coordinates of vertex, we will get:

$y=a(x-2)^2+3$

To find the value of a, we will substitute coordinates of point (0, -1) as:

$-1=a(0-2)^2+3$

$-1=a(4)+3$

$-1=4a+3$

$-1-3=4a+3-3$

$-4=4a$

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

$-1=a$

Therefore, our required equation would be $y=-1(x-2)^2+3$.