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Write the equation of the quadratic function with roots -10 and -8 and a vertex at (-9,...

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user6516700 | eNotes Newbie

Posted February 5, 2013 at 2:32 AM via web

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Write the equation of the quadratic function with roots -10 and -8 and a vertex at (-9, -1).

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jgeertz | College Teacher | (Level 1) Associate Educator

Posted February 5, 2013 at 6:04 AM (Answer #1)

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Write the quadratic equation whose roots are -10 and -8 with a vertex of (-9, -1).

Quadratic equations are in the form `ax^2 +bx+c=0` where a,b, and c are real numbers and a is not equal to 0.

Here we work backwards.

The roots are given as

`x=-10 `

`x=-8`

So we know

`(x+10)(x+8)=0`

FOIL to get

`x^2+18x+80 =0`

`` The vertex is the minimum or maximum point of the parabola represented by the quadratic equation.

The x coordinate of the vertex =`-b/(2a)`

 

```x=-18/(2(1))`  = -9

The y coordinate of the vertex can be found by substituting the value for x into the equation `y=ax^2+bx+c`

`y=(1)(-9)^2 +18(-9) +80`

`y=81-162+80`

`y=-1`

Thus the quadratic equation whose roots are -10 and -8 with a vertex of (-9,-1) is `x^2+18x+80=0`

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