Quadratic Eqn for parabola through (0,0), (-1,7), (6,42)

[megan0430]

Write a VERTEX form equation that is represented in:

Passes through the points: (0,0), (-1,7), and (6, 42).

PLEASE HELP!
gracias <3

 

[arthur ohlsten]

y=ax^2+bx+c

eq1 [let x=0 y=0] 0=c answer

eq2 [ let x=-1 y=7] we know c=0
eq2 7=a-b

eq3 [let x=6 y=42]
eq3 42=36a+6b

we have two equations in two unknowns (a and b) solve them

many ways to do this. my favorite way
7=a-b
42 =36a+6b multiply first equation by 6

42=6a-6b
42=36a+6b add the equations
-------------
84=42a
a=2 answer

from 7=a-b
7=2-b
b=-5 answer

y=2x^2-5x answer a parabola complete the square
y=2[x^2-5/2 x]
y=2[x^2-5/2 x + 25/16]-50/16
y=2[x+5/4]^2 -25/8 a parabola
open up
vertex at -5/4,-25/8
axis of symetry x=-5/4

I hope this is what you need
please check for math errors
Arthur