1) To find an equation of a parabola you need to know three points.
Find the equation of a parabola that passes through (0, 3), (-2, 7) and (1, 4).
X -> 0 , -2 , 1
Y -> 3 , 7 , 4
ax² + bx + c = y
(0,3) -> 0+0+c=3 -> c=3
(1,4) -> a+b+3=4 -> a+b=1 -> a = 1-b
(-2,7) -> 4a-2b+3=4 -> 4a-2b=4
-> 4a-2b=1 -> 4(1-b)-2b=4 -> b=0
-> a=1-B = 1-0=1
Y = ax² + bx + c
Y =1x² + ox + 3= x² + 3
Find the equation of a parabola that passes through (0, 3), (-2, 7) and (1, 4).
X -> 0 , -2 , 1
Y -> 3 , 7 , 4
ax² + bx + c = y
(0,3) -> 0+0+c=3 -> c=3
(1,4) -> a+b+3=4 -> a+b=1 -> a = 1-b
(-2,7) -> 4a-2b+3=4 -> 4a-2b=4
-> 4a-2b=1 -> 4(1-b)-2b=4 -> b=0
-> a=1-B = 1-0=1
Y = ax² + bx + c
Y =1x² + ox + 3= x² + 3
3) The path of any thrown ball is parabola. Suppose a ball is thrown from ground level, reach a maximum height of 20 meters of and hits the ground 80 meters from where it was thrown. Find the equation of the parabolic path of the ball; assume the focus is on the ground level.
#It opens down
*Vertex = (0,20)
* focus = (0,0)
*p= 20
*∣a∣ = ⅟₈₀
*Y = -⅟₈₀ (x)² +2
#It opens down
*Vertex = (0,20)
* focus = (0,0)
*p= 20
*∣a∣ = ⅟₈₀
*Y = -⅟₈₀ (x)² +2