SOLUTION: Write the equation of a parabola that as a vertical axis and passes through the origin, (3,-2), and (-2,2).
Algebra.Com
Question 636143: Write the equation of a parabola that as a vertical axis and passes through the origin, (3,-2), and (-2,2).
Found 2 solutions by lwsshak3, solver91311:
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Write the equation of a parabola that as a vertical axis and passes through the origin, (3,-2), and (-2,2).
**
Standard form of parabola with vertical axis of symmetry: y=A(x-h)^2+k, (h,k)=(x,y) coordinates of vertex.
For given parabola:
h=0
equation:
y=Ax^2+k
use given coordinates, (3,-2) and (-2,2), to solve for A and k
..
-2=3^2A+k
2=(-2)^2A+k
..
-2=9A+k
2=4A+k
subtract
5A=-4
A=-4/5
k=2-4A
=2-4*-4/5
=2+16/5
=10/5+16/5
=26/5
equation: y=-4x^2/5+26/5
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
A parabola is represented by a general form quadratic function: \ =\ ax^2\ +\ bx\ +\ c)
.
If it passes through a point )
, then the following will hold:
^2\ +\ b\left(x_i\right)\ +\ c)
For the three points you were given:
^2\ +\ b(0)\ +\ c\ =\ 0)
^2\ +\ b(3)\ +\ c\ =\ -2)
^2\ +\ b(-2)\ +\ c\ =\ 2)
From which the following 3X3 system can be derived:
Substituting the first into the other two gives us a 2X2 linear system:
Solve the 2X2 by whatever means you find convenient and then you will have the coefficients for your function.
John
My calculator said it, I believe it, that settles it
RELATED QUESTIONS
Determine the equation of the parabola that has its vertex at the origin and satisfies... (answered by josgarithmetic)
1.) write the equation of a vertical line passing through the point (6,2)
2.) write the... (answered by josgarithmetic)
Write the equation of the line that has a slope of negative 2 and passes through the... (answered by Edwin McCravy)
This is tricky for me, A parabola has a vertical axis and passes through the points... (answered by scott8148)
find the equation of the parabola with vertical axis that passes through the point (0,2)... (answered by Alan3354)
How do I determine the equation of the parabola that has vertex at the origin, axis of... (answered by lwsshak3)
FIND THE EQUATION OF THE PARABOLA WITH VERTICAL AXIS THAT PASSES THROUGH THE POINT (0,2)... (answered by josgarithmetic)
FIND THE EQUATION OF THE PARABOLA WITH VERTICAL AXIS THAT PASSES THROUGH THE POINT (0,2)... (answered by MathLover1)
A parabola has a axis of symmetry x=2 and passes through the points (0,7) and (-1,-3)... (answered by solver91311)
