Evaluate the expression x2 + y2 if x = -3 and y= -2
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<h3>Answer:</h3>
y = -3(x -2)² -5
<h3>Explanation:</h3>The equation of a parabola with vertex (h, k) is given by ...
... y = a(x -h)² +k . . . . . . . for some vertical scale factor "a".
We can find the value of "a" by substituting the coordinates of a point that is not the vertex. Here, that point is the y-intercept: (0, -17).
... y = a(x -2)² -5 . . . . . initial form of the equation for the parabola
... -17 = a(-2)² -5 . . . . . substitute y-intercept values
... -12 = 4a . . . . . . . . . . add 5, simplify
... -12/4 = a = -3
The desired equation is ... y = -3(x -2)² -5.