Question

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

Answer 1

The equation of (y-k)=a(x-h)² , where (h , k) are the coordinates of the vertex, which is given Vertex(-4,7) →y-7 = a(x+4)². To find the equation we have to calculate the coefficient a.  The roots are given x = -1 and x = -7. For
x= -1 or x=-7, y=0. Chose any of the roots and plug it in the equation:
y-7 = a(x+4)²
0-7 = a(-1+4)²→ - 7 = 9a and a = -7/9 (you will have same a if you choose x=-7.
Now the equation is y-7 = -7/9(x+4)² and after expanding:
y= (1/9)(-7x²-56x-49)