Question 775143
Q:
The vertex of this parabola is at (-2,-3). When the x-value is -1, the y-value is -5. What is the coefficient of the squared expression in the parabola's equation?
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A:
The vertex of parabola (quadratic function) with equation {{{y=a(x-h)^2+k}}} is (h,k).
If the vertex is (-2,-3), then h = -2, k = -3 and the quadratic function is {{{y=a(x+2)^2-3}}}. Substitute x = -1 and y = -5.
{{{-5=a(-1+2)^2-3}}}
-5 = a-3
a = -2
Therefore, {{{y = -2(x+2)^2-3}}} OR {{{y = -2x^2-8x-11}}}
The coefficient of the squared expression is {{{highlight(-2)}}}.