To find the vertex form of the quadratic function we need to make the function into y=a(x-h)^2+k where (h,k) is the vertex.
y=x^2+8x - 9
Knowledge about completing squares would help.
y+9 =x^2 + 8x Firstly move the constant to the other side, this can be done by adding 9 to both the sides.
We need to make x^2+8x into a whole square.
*In case you are confused with what a whole square is, it is nothing but expressing the given expression in the form (x-h)^2
On expanding (x-h)^2 would be x^2-2hx + h^2
Now let us see that the coefficient of x is 2h and we need h^2 so we divide coefficient of x by 2 and square the result to get h^2 That would help completing the square. The steps to complete the square for our question is given below.*
Divide the coefficient of x by 2 and square the result and add it to both the sides.
y+9 +(8/2)^2 = x^2 + 8x + (8/2)^2
y+9+16 = x^2 + 8x + 16
y+25= (x+4)^2
y=(x+4)^2 - 25 Vertex form
