SOLUTION: find the equation of a quadric function with x- intercepts (2,0) and (-7,0) and y intercept (0,5) please i need help for this problem please i need help i have exam on Tuesday 0

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: find the equation of a quadric function with x- intercepts (2,0) and (-7,0) and y intercept (0,5) please i need help for this problem please i need help i have exam on Tuesday 0      Log On


   

Question 194493: find the equation of a quadric function with x- intercepts (2,0) and (-7,0) and y intercept (0,5)
please i need help for this problem please i need help i have exam on Tuesday 05/07/09 so it is urgent!!!!!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since the equation has the x- intercepts (2,0) and (-7,0), this means that the roots are x=2 or x=-7


x=2 or x=-7 Start with the given roots.


x-2=0 or x%2B7=0 Get everything to the left side.


a%28x-2%29%28x%2B7%29=0 Combine the equations using the zero product property. Also, insert the variable "a" (this will be used to make the graph have a y-intercept of (0,5))


a%28x%5E2%2B5x-14%29=0 FOIL



So the general equation with the x- intercepts (2,0) and (-7,0) is: y=a%28x%5E2%2B5x-14%29



y=a%28x%5E2%2B5x-14%29 Start with the given equation.


y=ax%5E2%2B5ax-14a Distribute


5=a%2A0%5E2%2B5a%280%29-14a Plug in x=0 and y=5 (from the point (0,5))


5=-14a Multiply and simplify


5%2F%28-14%29=a Divide both sides by -14.


a=-5%2F14 Reduce and rearrange the equation.



y=ax%5E2%2B5ax-14a Go back to the previous equation


y=-%285%2F14%29x%5E2%2B5%28-5%2F14%29x-14%28-5%2F14%29 Plug in a=-5%2F14


y=-%285%2F14%29%2Ax%5E2-%2825%2F14%29x%2B5 Multiply and simplify



So the quadratic equation is y=-%285%2F14%29%2Ax%5E2-%2825%2F14%29x%2B5


Here's a graph to visually confirm the answer: