What is the quadratic function that is created with roots

Question

-10 and -4 and a vertex at (-7, -9)?

Answer 1

Roots of quadratic function : a = -10 , b = - 4

Vertex = ( -7 , -9 )

General quadratic function with roots is, y = k(x - a)(x - b)

Substitute : a = -10 , b = - 4

y = k(x - (-10))(x - (-4))

y = k(x + 10)(x + 4)                 ------------------------------------ (1)

The curve y = k(x + 10)(x + 4) is passes through vertex ( -7 , -9 ).

-9 = k(-7 + 10)(-7 + 4)

-9 = k(3)(-3)

k = 1

Substitute k = 1 in equation (1)

y = 1(x + 10)(x + 4)

y = (x² + 10x + 4x + 40)

y = x² + 14x + 40

Solution :

The quadratic function is y = x² + 14x + 40.