Question

Please help! Medal will be given.

A parabola contains the points (1,8), (4, 29), and (-3, 8). What is the equation of this parabola in standard form?

Answer 1

standard form is ax^2 + bx + c = 0

plug in the given values of x and y ( these are in the coordinates)

to get 3 equations in a, b and c
solve this sytem of equations and you have it

Answer 2

@welshfella - I did that but I don't think I did it correctly.

Here's my work:
8 = a + b + c
29 = 16a + 4b + c
8 = 9a - 4b + c
-----------------------
8 = a + b + c
-c + 8 = a + b
-c = -8 + a + b
c = 8 - a - b
------------------------
29 = 16a + 4b + 8 - a - b
29 = 15a +3b + 8
21 = 15a + 3b
------------------------
8 = 9a - 4b + 8 - a - b
8 = 8a - 3b + 8
0 = 8a - 3b
-------------------------
21 = 15a + 3b
-3b = -21 + 15a
b = 7 + 15a
(I made an error. It should be b = 7 - 5a)
-------------------------
a = 0
b = 7
c = 1

Answer 3

8 = 9a - 4b + c ?????

Answer 4

@IrishBoy123 - I think I did the problem wrong. Can you help me?

Answer 5

go back and correct that mistake (in line 3), the just follow ot through again, and you might well have got it right.

Answer 6

@IrishBoy123 - It should be 8 = 9a - 3b + c, right?

Answer 7

yes.

Answer 8

your 3rd equation is mistyped and it should be -3b instead of -4b:
so you get a=1, b=2, c=5
then \[x ^{2}+2x+5\]

Answer 9

@mlearning24 - Thank you.