# Demonstrate that vertex of parabolla x^2-4x+9 is on line x+y=7.

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### 2 Answers

You need to evaluate the coordinates of vertex using the formula:

`x = -b/(2a) ; y = -Delta/(4a)`

You need to identify the coefficients a,b,c such that:

`a = 1 ; b = -4 ; c = 9`

You need to substitute these values in formulas above such that:

`x = -(-4)/2 => x = 2`

You need to remember the formula of `Delta` such that:

`Delta = b^2 - 4ac => Delta = 16 - 36 => Delta = -20`

`y = -(-20)/4 => y = 5`

You need to substitute 2 for x and 5 for y in the given equation of the line such that:

`x + y = 7 => 2 + 5 = 7 => 7 = 7`

**Notice that the coordinates of vertex of parabola verify the equation of the line, hence, the vertex `(2;5)` lies on the line `x + y = 7.` **

`x^2-4x+9`

`a=1 b=-4 c=9`

use the formula `-b/(2a)` to find x

`x=4/(2xx1)` `x=4/2 ` `x=2`

plug in the x into the equation

`y= 2^2-4(2)+9 `

`y= 4-8+9`

`4-8= -4 ` `-4+9=5 ` `y=5`

the vertex is `(2,5)`