SOLUTION: A parabola cuts the x-axis at 1 and 3 and the y-axis at 6. Make up the equation of the parabola and sketch the parabola showing clearly the turning point.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A parabola cuts the x-axis at 1 and 3 and the y-axis at 6. Make up the equation of the parabola and sketch the parabola showing clearly the turning point.      Log On


   

Question 824721: A parabola cuts the x-axis at 1 and 3 and the y-axis at 6. Make up the equation of the parabola and sketch the parabola showing clearly the turning point.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A parabola cuts the x-axis at 1 and 3 and the y-axis at 6.
Make up the equation of the parabola and sketch the parabola showing clearly the turning point.
:
From the x intercepts we have two factors
(x-1)(x-3) Foils to x^2 - 3x - x + 3
multiply equation by 2 to get a y intercept of 6
y = 2x^2 - 8x + 6, is the equation
looks like this
+graph%28+300%2C+200%2C+-4%2C+5%2C+-10%2C+10%2C+2x%5E2-8x%2B6%29+
you can see the turning point at the axis of symmetry is x=2
find y
y = 2(2^2) - 8(2) + 6
y = 8 - 16 + 6
y = -2