Determine the equation of a parabola with a vertex of (-3,4) and passes through (-1,1)
To determine the equation of a parabola with a vertex of (-3,4) and passing through (-1,1), we can use the vertex form of a parabolic equation, which is given by:
y = a(x - h)^2 + k
where (h, k) represents the vertex of the parabola.
Plugging in the vertex given as (-3,4), we can rewrite the equation as:
y = a(x + 3)^2 + 4
Now, to find the value of 'a', we can use the fact that the parabola passes through the point (-1,1). Plugging in these values, we get:
1 = a(-1 + 3)^2 + 4
Simplifying this equation further, we have:
1 = a(2)^2 + 4
1 = 4a + 4
Subtracting 4 from both sides gives:
-3 = 4a
Dividing both sides by 4, we have:
a = -3/4
Now that we have the value of 'a', we can plug it back into the equation:
y = (-3/4)(x + 3)^2 + 4
Therefore, the equation of the parabola with a vertex of (-3,4) and passing through (-1,1) is:
y = (-3/4)(x + 3)^2 + 4