SOLUTION: Write the equation of the quadratic function with roots -1 and -7 and a vertex at (-4, 7)

Algebra ->  Systems-of-equations -> SOLUTION: Write the equation of the quadratic function with roots -1 and -7 and a vertex at (-4, 7)      Log On


   

Question 877935: Write the equation of the quadratic function with roots -1 and -7 and a vertex at (-4, 7)
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Try a parabola.
y=a%28x%2B1%29%28x%2B7%29, accounts for the roots.

Notice that -4 is in the middle of -1 and -7. Notice that y=7 is greater than the x-axis. The parabola's vertex is a maximum, and a%3C0.

Solve symbolically for a.
a=y%2F%28%28x%2B1%29%28x%2B7%29%29
Use coordinates of vertex.
a=7%2F%28%28-4%2B1%29%28-4%2B7%29%29
a=7%2F%28-3%2A3%29
a=-7%2F9

Equation: highlight%28y=-%287%2F9%29%28x%2B1%29%28x%2B7%29%29