Answer:
Let y=ax^2+bx+c be the equation of the parabola. Set up equations.
Using (0,5). 5=a(0)2+b(0)+c
5
=
a
(
0
)
2
+
b
(
0
)
+
c
Using (2,15), 15=a(2)2+b(2)+5
15
=
a
(
2
)
2
+
b
(
2
)
+
5
4a+2b=10
2a+b=5
Using (4,9)
9=a(4)2+b(4)+5
9
=
a
(
4
)
2
+
b
(
4
)
+
5
16a+4b=4
4a+b=1
Subtract each side of (1) and (2) to eliminate b and solve for a: -2a=4
a=-2
Solve for b using (1): 2(-2)+b=5
-4+b=5
b=9
So, the equation is y=−2x2+9x+5
Step-by-step explanation:
