SOLUTION: A.) What is an equation of the parabola with vertex at the origin and focus (-5,0)? B.) what are the vertex, focus, and directrix of the parabola with equation y=x^2-6x+15.

Question 755236: A.) What is an equation of the parabola with vertex at the origin and focus (-5,0)?

B.) what are the vertex, focus, and directrix of the parabola with equation y=x^2-6x+15.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
A.) What is an equation of the parabola with vertex at the origin and focus (-5,0)?
Basic equation for a parabola that opens leftward with vertex at (0,0): y^2=-4px
p=5
4p=20
Equation for given parabola: y^2=-20x
..
B.) what are the vertex, focus, and directrix of the parabola with equation
y=x^2-6x+15.
complete the square
y=(x^2-6x+9)-9+15
y=(x-3)^2+6
(x-3)^2=(y-6)
This is an equation of a parabola that opens upward.
Its basic equation: (x-h)^2=4p(y-k)
For given equation: y=x^2-6x+15
vertex: (3,6)
axis of symmetry: x=3
4p=1
p=1/4
focus: (3, 25/4) (p-distance above vertex on the axis of symmetry)
diectrix: y=23/4 (p-distance below vertex on the axis of symmetry)
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