Question

equation of the parabola in vertex form that passes through (4,-7) and has a vertex of (1,-6)

Answer 1

$y = -\frac{1}{9}(x - 1)^2 - 6$

Step-by-step explanation:

The vertex form of the equation for a parabola is given by

$y = a(x - h)^2 + k$

where (h, k) are the coordinates of the parabola's vertex. Since the vertex is at (1, -6), we can write the equation as

$y = a(x - 1)^2 - 6$

Also, since the parabola passes through (4, -7), we can use this to find the value for a:

$-7 = a(4 - 1)^2 - 6 \Rightarrow -7 = 9a - 6$

or

$a = -\frac{1}{9}$

Therefore, the equation of the parabola is

$y = -\frac{1}{9}(x - 1)^2 - 6$