SOLUTION: Please help me solve this problem: Let f be a quadratic function. The slope of the tangent line to the graph of f at x = 1 is 3, and the slope of the tangent line can be drawn to

Algebra ->  Test -> SOLUTION: Please help me solve this problem: Let f be a quadratic function. The slope of the tangent line to the graph of f at x = 1 is 3, and the slope of the tangent line can be drawn to      Log On


   

Question 1028821: Please help me solve this problem:
Let f be a quadratic function. The slope of the tangent line to the graph of f at x = 1 is 3, and the slope of the tangent line can be drawn to the graph of f at x = 2 is 5. If the graph of f passes through the point (1,0), find the equation of f.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
For a quadratic equation,
y=ax%5E2%2Bbx%2Bc
The slope of the tangent line is equal to the derivative,
m=dy%2Fdx=2ax%2Bb
So then, x=1, m=3
3=2a%281%29%2Bb
1.2a%2Bb=3
.
.
When x=2, m=5
5=2a%282%29%2Bb
2.4a%2Bb=5
Subtracting eq. 1 from eq. 2,
4a%2Bb-2a-b=5-3
2a=2
a=1
Then,
2%281%29%2Bb=3
2%2Bb=3
b=1
So then using the last point,
y=x%5E2%2Bx%2Bc
0=2%281%29%5E2%2B1%2Bc
0=2%2B1%2Bc
0=3%2Bc
c=-3
.
.
y=x%5E2%2Bx-2
.
..
.