Given:
Direction opens up with minimum at -2
Passes through (0,0) and (2,0)
Write the equation of the parabola.
Let y = a(x - p)² + q
The q value of vertex is -2, so
y = a(x - p)² - 2
What do I do next? Pass through the points? How to solve this?
Thanks.
Hello, shenton!
Given: opens up with minimum at -2
Passes through (0,0) and (2,0)
Write the equation of the parabola.
The general equation of a "vertical" parabola is: .
We have three points: . . . . and the vertex:
. . If you plot the two points, you see they are x-intercepts.
. . The axis of symmetry lies halfway between them at
. . And that is how I located the vertex.
Substitute the points into the general equation.
Divide (2) by 2: .
. . Subtract (3): .
. .And we have: .
Substitute into (3): .
Therefore, the equation of the parabola is: .