Final answer:
To find the equation of a parabola with a vertex (-8,-7) that passes through (-7,-9), we use the vertex form of a parabola equation and plug in the values of the vertex and the given point to find the value of 'a'. The final equation of the parabola is y = -2(x+8)^2-7.
Step-by-step explanation:
To find the equation of a parabola with a vertex (-8,-7) that passes through (-7,-9), we can use the vertex form of a parabola equation: y = a(x-h)^2+k, where (h,k) is the vertex. Plug in the values of the vertex: h = -8 and k = -7. The equation becomes y = a(x+8)^2-7. Next, use the point (-7,-9) to find the value of 'a'. Substitute -7 for 'y' and -7 for 'x' in the equation and solve for 'a'.
-9 = a(-7+8)^2-7
-9 = a(1)^2-7
-9 = a-7
a = -2
Finally, substitute the value of 'a' back into the equation to get the final equation of the parabola: y = -2(x+8)^2-7.