SOLUTION: I have been working on this math problem and I can't figure it out. I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!! Writing Qua

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I have been working on this math problem and I can't figure it out. I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!! Writing Qua      Log On


   

Question 183833This question is from textbook Algebra and Trigonometry Structure and Method book 2
: I have been working on this math problem and I can't figure it out. I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!!

Writing Quadratic Equations and Functions
Find a quadratic function F(x)=ax^2+bx+c for each parabola described.
y-intercept 2; x-intercepts 1 and 5 This question is from textbook Algebra and Trigonometry Structure and Method book 2

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The y-intercept occurs where x=0, so
y%280%29+=+2 and
y%280%29+=+a%2A0%5E2%2Bb%2A0%2Bc+
y%280%29+=+c so,
c+=+2
The x-intercepts are the roots
For a quadratic, where y+=+0
ax%5E2%2Bbx%2Bc+=+0+
The roots occur at
x+=+r%5B1%5D
x+=+r%5B2%5D
%28x+-+r%5B1%5D%29%28x+-+r%5B2%5D%29+=+0 (If x+=+r%5B1%5D or x+=+r%5B2%5D, then
this is true)
given:
r%5B1%5D+=+1
r%5B2%5D+=+5 so,
%28x+-+1%29%28x+-+5%29+=+0
x%5E2+-+6x+%2B+5+=+0
Multiply both sides by 2%2F5
%282%2F5%29%2Ax%5E2+-+%2812%2F5%29%2Ax+%2B+2+=+0 answer
I'll plot this