Question

Write an equation of the parabola in vertex form.

Answer 1

Answer:

$y= -\frac19(x-3)^2+1$

Step-by-step explanation:

the x-3 is to shift a normal parabola 3 to the right

the +1 is to lift the top up by one

the -1/9 is to compress and swapt it around

Answer 2

Answer:

y =-  $\frac{1}{9}$(x - 3)² + 1

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (3, 1) , thus

y = a(x - 3)² + 1

To find a substitute another point on the graph into the equation

Substitute (1, $\frac{5}{9}$ ) into the equation

$\frac{5}{9}$ = a(1 - 3)² + 1 ( subtract 1 from both sides )

- $\frac{4}{9}$ = 4a ( divide both sides by 4 )

a = - $\frac{1}{9}$

y = - $\frac{1}{9}$ (x - 3)² + 1 ← equation of parabola in vertex form