The vertex of this parabola is at (4, - 3). When the x-value is 5, the

y-value is - 6. What is the coefficient of the squared expression in the parabola's equation?

Parabola equation with a vertex at (h, k) is given by y = a (x - h) ^2 + k

For the give parabola, y = a (x - 4) ^2 - 3

y = a (x^2 - 8x + 16) - 3

At (5, - 6)

-6 = a ((5) ^2 - 8 (5) + 16) - 3 = a (25 - 40 + 16) - 3 = a - 3

a = - 6 + 3 = - 3

Therefore, the coefficient of the squared expression is - 3.