The vertex form of a quadratic function is given by:
y = a(x - h)^2 + k
where (h, k) is the vertex of the parabola.
Using the given vertex points (-3, -4) and (-2, -3), we can plug these values into the equation:
-4 = a(-3 - h)^2 + k
-3 = a(-2 - h)^2 + k
Substitute (-3, -4) into the first equation:
-4 = a(-3 - h)^2 + k
-4 = a(9 + 6h + h^2) + k
-4 = 9a + 6ah + ah^2 + k
Substitute (-2, -3) into the second equation:
-3 = a(-2 - h)^2 + k
-3 = a(4 + 4h + h^2) + k
-3 = 4a + 4ah + ah^2 + k
Now we have a system of equations:
-4 = 9a + 6ah + ah^2 + k
-3 = 4a + 4ah + ah^2 + k
Subtract the second equation from the first equation:
-1 = 5a + 2ah + k
Now we have a system of two equations:
-1 = 5a + 2ah + k
-4 = 9a + 6ah + k
Solve this system of equations to find the value of 'a', 'h', and 'k' to get the vertex form of the function.
What is the equation in vertex form for the function?
The vertex form is (-3, -4) and (-2, -3)
1 answer
1 answer