# How do you find the vertex of the parabola #y = x^2 - 4x#?

##### 2 Answers

#### Explanation:

The easiest way is:

axis on symmetry is:

Vertex is:

c = y-intercept

so your function:

a = 1

b = -4

c = 0

f(aos) means we put the aos back in your function as x and solve for y:

Vertex is:

Vertex is:

Note, this can also be solved by completing the square and converting the function to vertex form.

graph{y = x^2 - 4x [-7.13, 12.87, -7.8, 2.2]}

#### Explanation:

#"the vertex lies on the axis of symmetry which is"#

#"situated at the midpoint of the zeros"#

#"to find the zeros set y = 0"#

#rArrx^2-4x=0larrcolor(blue)"factorise"#

#rArrx(x-4)=0#

#"equate each factor to zero and solve for x"#

#rArrx=0#

#x-4=0rArrx=4#

#"axis of symmetry/x-coordinate of vertex "=(0+4)/2=2#

#"substitute this value into the equation for y"#

#rArry=2^2-(4xx2)=4-8=-4#

#rArrcolor(magenta)"vertex "=(2,-4)#

graph{(y-x^2+4x)((x-2)^2+(y+4)^2-0.04)=0 [-10, 10, -5, 5]}