SOLUTION: A parabola with an equation of the form y = ax^2 + bx + c has the point (-2, 1) as its vertex. If (-4, 5) also lies on the parabola, which of the following is another point on th

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A parabola with an equation of the form y = ax^2 + bx + c has the point (-2, 1) as its vertex. If (-4, 5) also lies on the parabola, which of the following is another point on th      Log On


   

Question 366485: A parabola with an equation of the form y = ax^2 + bx + c has the point (-2, 1) as its vertex. If (-4, 5) also lies on the parabola, which of the following is
another point on this parabola?
(A) (-4, 3) (B) (-1, 3) (C) (0, 5) (D) (2, 1) (E) (4, 5)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Since the vertex occurs at (-2,1), the line of symmetry is x=-2.
Since (-4,5) is a point on the line, find the x value equidistant from the line of symmetry.
The x-distance from (-4,5) to the line of symmetry is d%5Bx%5D=-2-%28-4%29=2.
Then add d%5Bx%5D=2 to the x position of the line of symmetry x position to get the point symmetric to (-4,5).
x%5B2%5D=-2%2B2=0
y%5B2%5D=5
.
.
(0,5) is another point on the parabola.
.
.
.