Give the vertex, axis of symmetry,domain,and range.

Question

f(x)=x^2-6x+5

Answer 1

 The function f (x ) = x²  - 6x  + 5

y  = x²  - 6x + 5

Compare it to parabola equation y = ax²  + bx + c

a  = 1, b  = - 6, c  = 5

Axis of symmetry is x coordinate of vertex.

• Axis of symmetry x  = -b/2a

x  = -(-6)/2(1) = 3

Axis of symmetry x  = 3.

To find y  coordinate of vertex substitute x  = 3 in y  = x²  - 6x  + 5.

y  = (3)²  - 6(3) + 5.

y  = 9 - 18 + 5

y  = -4

Vertex (h , k ) = (x , y ) = (3, -4)

a  is positive number the parabola opens up and has minimum value.

When the parabola opens up it has a minimum point which is the vertex of parabola (3, -4)

We know that domain of the function is all possible x  values and range is all posible y  values.

 parabola domain x  =  all real numbers.

In the minimum point y  = -4  so the graph of parabola cannot be lower than -4.

Thus the range of function y  ≥ -4.

Domain of function is all real numbers.

Range of the function is  {y |y  ≥ -4}.