Which is an equation for the parabola that has vertex (-3, 1) and passes through the point (-2, 4)?
The vertex form is
y = a(x - h) ^2 + k where (h, k) is the vertex and (x,y) is a point on the graph
4 = a ( -2- -3)^2 + 1 subtract 1 from both sides
3 = a ( 1)^2
3 = a (1)
a = 3
So...the equation is
y = 3 ( x + 3)^2 + 1
The equation of the parabola with vertex (h,k)(h,k) is y=a(−h+x)^2+ky=a(−h+x)^2+k.
Thus, the equation of the parabola is y=a(x+3)^2+1y=a(x+3)^2+1.
To find a, use the fact that the parabola passes through the point (−2,4)(−2,4): 4=a+14=a+1.
Solving this equation, we get that a=3a=3.
Thus, the equation of the parabola is y=3(x+3)2+1y=3(x+3)^2+1.
I used parabola calculator.
Hope it helps!