write the standard form equation of the parabola with vertex (-2,-2) that goes through point (-1,0)
y= a (x-b)^2 + c
b has to be -2, that gives the shift to the left.
y=a( x+2)^2 + c
when x=-2, y=-2, that makes c -2
y=a( x+2)^2 -2
finally, put the point -1,0 in to find a.
To find the value of "a", plug in the coordinates of the given point (-1,0) into the equation:
0 = a(-1 + 2)^2 - 2
Simplifying this equation, we get:
0 = a(1)^2 - 2
0 = a - 2
Adding 2 to both sides of the equation, we find:
2 = a
Therefore, the value of "a" is 2.
Now we can substitute the values of "a", "b", and "c" into the equation:
y = 2(x + 2)^2 - 2
This is the standard form equation of the parabola with a vertex at (-2,-2) that passes through the point (-1,0).