Question 186277: Hi my name is Brandie. My teacher gave me a math problem to day and I can't get it. The problem is:
The table is for a quadratic equation-
x, y
-3, 0
-2, -7
-1, -8
0, -3
1, ?
Determine the quadratic equation using the information from the table. And solve for '?'. I don't understand how I'm suppose to do this. Can you because help me. This is the only problem I can't get.
Found 2 solutions by ankor@dixie-net.com, stanbon:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The table is for a quadratic equation-
x, y
-3, 0
-2, -7
-1, -8
0, -3
1, ?
Determine the quadratic equation using the information from the table. And solve for '?'.
:
Using the form: ax^2 + bx + c = y solve for a, b, c
c is the y intercept (x=0), notice in the table when x=0, y = -3
therefore we know that c = -3
:
Solve for a and b, take the values for x and y from the given table:
;
when x=-3; y=0
(-3^2)a + (-3)b - 3 = 0
9a - 3b = +3
simplify, divide equation by 3:
3a - b = 1
:
when x=-1, y=-8
(-1^2)a + (-1)b - 3 = -8
a - b = -8 + 3
a - b = -5
:
Use these two equations for elimination
3a - b = 1
a - b = -5
---------------subtraction eliminates b, find a
2a = +6
a = 3
:
Find b using 3a - b = 1, substitute 3 for a
3(3) - b = 1
9 - b = 1
-b = 1 - 9
-b = -8
b = +8
:
The quadratic equation; y = 3x^2 + 8x - 3
You can check to see if this is true
substitute the given x values in the equation, see if it = y
:
Regarding the question mark, find y when x = 1"
y = 3(1^2) + 8(1) - 3
y = 3 + 8 - 3
y? = 8
:
:
Did this make sense to you?
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! The table is for a quadratic equation-
x, y
-3, 0
-2, -7
-1, -8
0, -3
1, ?
Determine the quadratic equation using the information from the table. And solve for '?'.
----------------
Quadratic form: y = ax^2 + bx + c
Using (0,-3) you get -3 = a*0 + b*0 + c
So c = -3
----------------------
You now know y = ax^2 + bx -3
---------------
Substitute two of the point values into the form to solve for a and b.
Using (-3,0) you get: a(-3)^2 + b(-3) -3 = 0
Using (-2,-7) you get: a(-2)^2 + b(-2) - 3 = -7
-------------------------------
Simplify these equations:
9a - 3b = 3
4a - 2b = -4
-----------------
Modify:
18a - 6b = 6
12a - 6b = -12
---------------
Subtract to solve for "a":
6a = 18
a = 3
------
Substitute into 4a - 2b = -4 to solve for "b":
12 - 2b = -4
-2b = -16
b = 8
--------------------
Equation: y = 3x^2 + 8x -3
====================================
Find "?".
f(1) = 3*1 + 8*1 -3 = 8
====================================
Cheers,
Stan H.
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