SOLUTION: Find the rule of a quadratic function (in general form) whose graph has x intercepts at x=7 and x=-3 and a y-intercept at y=5.

Algebra ->  Equations -> SOLUTION: Find the rule of a quadratic function (in general form) whose graph has x intercepts at x=7 and x=-3 and a y-intercept at y=5.      Log On


   

Question 850501: Find the rule of a quadratic function (in general form) whose graph has x intercepts at x=7 and x=-3 and a y-intercept at y=5.
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
Standard Form: y=a%28x-h%29%5E2%2Bk, vertex at (h,k). This form is not really necessary here because the two zeros are given.

FACTORED FORM: y=a%28x-r%29%28x-s%29, and you can say, r=7 and s=-3.
y=a%28x-7%29%28x%2B3%29.
The use of the given y-intercept will let you find a.
a%28x-7%29%28x%2B3%29=5 occurs when x=0.
a%280-7%29%280%2B3%29=5
-21a=5
a=-5%2F21
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Equation is highlight%28y=-%285%2F21%29%28x-7%29%28x%2B3%29%29.
For GENERAL FORM, just multiply the expression on the right side.