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