For each x intercept the corresponding factor can be deduced. For x intercepts given at 1,2,3 , the equation can be written as
y= (x-1) (x-2) (x-3)
Because x=1 therefore x-1=0 , similarly x=2 , x-2=0 and , x=3 , x-3=0
or
y= x²+2x-3 (x-3)
or
y= x³+2x²-3x-3x²-6x+9
y= x³-x²-9x+9
So before I put the equation into standard form, I'm first going to be putting it into vertex form. Since the vertex appears to be (-1,7), plug that into the vertex form formula:
Next, we need to solve for a. Looking at this graph, another point that is in this line is the y-intercept (0,5). Plug (0,5) into the x and y placeholders and solve for a as such:
Now we know that <u>our vertex form equation is y = -2(x + 1)^2 + 7.</u>
However, we need to convert this into standard form still, and we can do it as such:
Firstly, solve the exponent:
Next, foil -2(x^2+2x+1):
Next, combine like terms and <u>your final answer will be: </u>