Suppose a parabola has vertex (–8, –7) and also passes through the point (–7, –4). Write the equation of the parabola in vertex form.
The vertex form of a parabola is given by:
y = a(x - h)^2 + k
where (h, k) is the vertex of the parabola.
Given that the vertex is (-8, -7), we can substitute these values into the equation we obtained earlier:
y = a(x - (-8))^2 + (-7)
Simplifying:
y = a(x + 8)^2 - 7
Now, we can use the point (–7, –4) to find the value of "a":
-4 = a(-7 + 8)^2 - 7
-4 = a(1)^2 - 7
-4 = a - 7
a = -4 + 7
a = 3
Substituting this value back into the equation:
y = 3(x + 8)^2 - 7
Therefore, the equation of the parabola in vertex form is y = 3(x + 8)^2 - 7.