Question 1114193
the standard form of your quadratic equation is:


y = ax^2 + bx + c


when x = -2 and y = -8, this equation becomes:


-8 = 4a -2b + c


when x = -4, this equation becomes:


-12 = 16a - 4b + c


when x = 1, this equation becomes:


13 = a + b + c


you have 3 equations thst need to be solved simultaneously.


they are:


-8 = 4a - 2b + c
-12 = 16a - 4b + c
13 = a + b + c


you can reorder the terms to get:


4a - 2b + c = -8
16a - 4b + c = -12
a + b + c = 13


they are now in standard linear equation form.


when you solve these equations simultaneously, you will find that:


a = 1
b = 8
c = 4


since the standard form of your equation is y = ax^2 + bx + c, you get:


y = x^2 + 8x + 4


that's your quadratic equation.


when x = -2, you get y = (-2)^2 - 8*2 + 4 = -8


when x = -4, you get y = (-4)^2 - 8*4 + 4 = -12


when x = 1, you get y = 1^2 - 8*1 + 4 = 13


this confirms your equation is correct.


i'm assuming you know how to solve 3 equations in 3 unknowns simultaneously.


i solved as follows.
reference the worksheet shown below.


<img src = "http://theo.x10hosting.com/2018/040802.jpg" alt="$$$" >


i started with equations 1, 2, and 3.
those are the circled numbers on the worksheet.


i then took equation 2 as is and multiplied equation 1 by 4 to get equation 4.


i then subtracted equation 4 from equation 2 to get equation 5.


i then took equation 2 as is and multiplied equation 3 by 16 to get equation 6.


i then subtracted equation 6 from equation 2 to get equation 7.


i then copied down equation 5 and 7 and proceeded to reduced these further so that i could solve for a single variable.


i multiplied equation 5 by 5 to get equation 8 and kept equation 7 as is.


i then subtracted equation 7 from equation 8 to get equation 9.


i then solved equation 9 for c to get c = 4


i then took equation 5 and replaced c with 4 and solved for b to get b = 8.


i then took equation 1 and replaced c with 4 and b with 8 and solved for a to get a = 1.


the result was a = 1, b = 8, c = 4.


that led to y = x^2 + 8x + 4, which is the solution shown above.