Question

Write the equation of the parabola in vertex form. vertex (2,1), point (3,- 1) f(x) =

Answer 1

Answer:

$f(x) = -2(x - 2)^2 + 1$

Step-by-step explanation:

Given the vertex, (2, 1) and point (3, -1):

We can plug in those values into the Vertex Form:

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

$f(x) = a(x - 2)^2 + 1$

Plug in the other point, (3, -1) into the equation to solve for a:

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

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

-1 = a1 + 1

Subtract 1 from both sides of the equation to solve for a:

-1 - 1 = 1a + 1 - 1

-2 = 1a

$\frac{-2}{1} = \frac{1a}{1}$

-2 = a

Therefore, the equation of the parabola in Vertex Form is:

$f(x) = -2(x - 2)^2 + 1$

where a = -2, and the vertex, (2, 1) as its maximum point.

Answer 2

Answer:

Step-by-step explanation:

Vertex form of parabola = a(x - h)^2 + k

                                          =  (3 - 2)^2 + 1

                                           = 1 + 1 = 2