Question

please use the answer in the attached picture to write down the co-ordinate of the turning point of x^2-5x+4

Answer 1

By general rule w ehave this property:

`(x-a)^2=x^2-2ax+a^2`

Using this expression we can do the following:

`(x-(5)/(2))^2-(9)/(4)=(x\cdot x^{}-2\cdot x\cdot(5)/(2)+(5)/(2)\cdot(5)/(2))-(9)/(4)=x^2-5x+(25)/(4)-(9)/(4)=x^2-5x+(16)/(4)=x^2-5x+4=(x-1)(x-4)`

Then the final simplfied form is:

(x-1)(x-4)

Then we can find the turning point like this:

`x=-(b)/(2a)=-(-5)/(2\cdot1)=(5)/(2)`

And the corresponding y coordinate is:

`((5)/(2)-(5)/(2))^2-(9)/(4)=-(9)/(4)`

Final answer:

`((5)/(2),-(9)/(4))`