what is x^2-6x+1

Question

x^2-6x+1 write each quadratic function in vertex form identify the vertex axis of symmetry and direction of opening

Answer 1

Given equation is f(x) = y = x^-6x+1

Standard parabola equaton is y = ax^2+bx+c

Compare the above equaton a = 1, b = -6, c = 1

→ axis of symmetry is x = -b/2a = -(-6)/2*1 = 3

To find y, substitute x = 3 in given equation.

y = 3^2-6*3+1

y = 9-18+1 = -8

→ Vertex of parabola is (3,-8)

Vertex form is y = a(x-h)^2+k

y = 1(x-3)^2-8

y = (x-3)^2-8

Parabola direction of opening is simply depends on it's (x-h)^2 coefficient "a" sign.

The sign is in given problem a = 1 is positive.

→ So the given parabola opens upward. It iis like U shape.