SOLUTION: Write a quadratic equation of the form y=ax^2+bx+c with the given x-intercepts (3,0) and (-1,0).

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Write a quadratic equation of the form y=ax^2+bx+c with the given x-intercepts (3,0) and (-1,0).      Log On


   

Question 1154181: Write a quadratic equation of the form y=ax^2+bx+c with the given x-intercepts
(3,0) and (-1,0).
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+
+0+=+%28+x+-+3+%29%2A%28+x+-%28-1%29+%29+
+0+=+x%5E2+-+3x+%2B+x+-+3+
+y+=+x%5E2+-+2x+-+3+
-----------------------------
check:
the x-value of the peak will be at
+x%5Bpk%5D+=+-b%2F%282a%29+
+x%5Bpk%5D+=+-%28-2%29+%2F+%282%2A1%29+
+x%5Bpk%5D+=+1+
This value should be at the midpoint of
(3,0) and (-1,0)
and
+y%5Bpk%5D+=+1%5E2+-+2%2A1+-+3+
+y%5Bpk%5D+=+-4+
+x%5Bpk%5D+ is at:
+%28+3+%2B%28-1%29+%29+%2F+2+=+1+
OK
Here's the plot:
+graph%28+400%2C+400%2C+-6%2C+6%2C+-6%2C+6%2C+x%5E2+-+2x+-+3+%29+