Answer:
y = -6x^2 + 15x -5
Step-by-step explanation:
equation step 1 for parabola
y2-y1 /x2-x1
= 1 - 4 / 0 - - 1
= -3 / 1
y = -3
We try again different points
y2-y1 / x2-x1
= 7 - 1 / 2 - 0
= 6 / 2
y = 3
we can see that one side is descending and 1 side is ascending
The start of the parabola is 0,1 as x = 0 and crosses the line.
we try again
y2-y1 /x2-x1
7-1 / 2-0
= 6 / 2
y = 3
You should know that a parabola is determined by 3 points, so unless your points happen to be collinear, they will determine a parabola. A straight forward, if not always the easiest way would be to take the general equation
y = ax^2 + bx + c
plug in each point, eg.y = y1 and x = x1 eg) y = y2 and x = y2 eg) y = y3 x=x3
Top equation re-used last see at end.
4 = a(-1)^2 + b(-1 ) + c = a+b+c=4
1 = a(0)^2 +b(0) + c = c =1
7 = a(2)^2 + b(2) + c = 4a+2b=7
a= -1-0 = -1 b = -1-0 = -1 and 4-1 = 3
-a +-b = 3
2nd set of equations
4a-0a = 4a
2b-0b = 2b
7-1 = 6
4a +2b=6 and previous
-a +-b = 3 here we can multiply by -2 to get 2b equality to 1st equation
2a + 2b = -6
4a + 2b = 6
2a = -12
2a = -12 / 2
a = -6
plug a
4(-6) + 2b = 6
-24 + 2b = 6
2b = 6 +24
2b = 30
b = 15
then put a + b+ c into top equation
(-6) + (15) + c = 4
9 + 0 = 4
9 -9 = 4 -9 cancel
c = -5
Then put into first equation as c and complete equation
To find that;
y = -6x^2 + 15x -5 = is our equation of the parabola.
This is how to solve your two linear equations in three unknowns.
