Answer:
The vertex form equation of a parabola is y = a(x - h)^2 + k, where (h, k) is the vertex and a is a constant that determines the shape of the parabola.
To write the vertex form equation of each parabola, we need to find the values of a, h, and k for each equation.
A. y = x^2 + 4 To find a, we can compare the coefficients of x^2 in the given equation and the vertex form equation. We see that a = 1 in this case.
To find h and k, we can complete the square for the x-term in the given equation. We add and subtract (b/2a)^2, where b is the coefficient of x and a is the coefficient of x^2.
y = x^2 + 4 y = x^2 + 4 + (0/2)^2 - (0/2)^2 y = x^2 + 4 + 0 - 0 y = (x + 0)^2 + 4 - 0 y = (x + 0)^2 + 4
We see that h = -0 and k = 4 in this case. The vertex form equation is y = (x + 0)^2 + 4, or y = x^2 + 4.
B. y = (x - 2)^2 + 4 This equation is already in vertex form, so we can directly read the values of a, h, and k. We see that a = 1, h = 2, and k = 4 in this case. The vertex form equation is y = (x - 2)^2 + 4.
C. y = (x + 4)^2 - 1 This equation is also already in vertex form, so we can directly read the values of a, h, and k. We see that a = 1, h = -4, and k = -1 in this case. The vertex form equation is y = (x + 4)^2 - 1.
D. y = (x + 4)^2 - 2 This equation is also already in vertex form, so we can directly read the values of a, h, and k. We see that a = 1, h = -4, and k = -2 in this case. The vertex form equation is y = (x + 4)^2 - 2.