Write an equation of each parabola in vertex form vertex : (1/2,1) point: (2,-8)

Question

asked Feb 8, 2023 56.3k views

1 Answer

Ingenious · Answer 1 · 2023-02-14T22:01:22+0000

Answer:
$y=-4 \left(x-(1)/(2) \right)^2 +1$

Explanation:

Using the vertex form, the equation is

$y=a \left(x-(1)/(2) \right)^2 +1$

Substituting in the coordinates (2, -8) to solve for a,

$-8=a \left(2-(1)/(2) \right)^2 +1\\\\-8=(9)/(4)a+1\\\\-9=(9)/(4)a\\\\a=-4$

So, the equation is
$y=-4 \left(x-(1)/(2) \right)^2 +1$