Question

write the equation of the parabola in vertex form.vertex (3,2), point (2,-2)

Answer 1

Answer:

$y=-4(x-3)^2+2$

Step-by-step explanation:

$y=a(x-p)^2+q$ - equation of the parabola in vertex form

from vertex (3,2) we know that $p=3, \ q=2$

from point (2,-2) we know that $x=2, \ y=-2$

inserting p=3, q=2, x=2 and y=-2 to the equation $y=a(x-p)^2+q$, we calculate $a$

$-2=a(2-3)^2+2\\ -2=a\cdot(-1)^2+2\\ -2=a\cdot1+2\\ -2=a+2\\ -2-2=a\\ -4=a\\ a=-4$

insert a=-4, p=3 and q=2 to the equation

$y=-4(x-3)^2+2$