a. Since the vertex form equation of a parabola is given by y = a(x-h)^2 + k, where (h,k) is the vertex, we can substitute the given vertex (-8, -7) into the equation to find a:
y = a(x+8)^2 - 7
Now, we need additional information to calculate the value of 'a'.
b. The distance between the vertex and the focus of a parabola is equal to the absolute value of the distance between the vertex and the directrix. Therefore, the directrix is a horizontal line that passes through (-8, -8) with the equation y = -8.
The standard form equation of a parabola that opens downwards is given by (y-k)^2 = 4a(x-h). Substituting the given values, we have:
(y+7)^2 = 4a(x+8)
Since the directrix is y = -8, the distance between the vertex and the directrix is 15 (|-7 - (-8)|).
This means that 4a = 15, so a = 15/4.
Now we can write the vertex form equation of the parabola:
y = (15/4)(x+8)^2 - 7
Use the information provided to write the vertex form equation of the parabola:
a. Vertex (-8, -7)
b. Focus: (-8, -6)
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