Find the Quadratic Equation (-2.75,-10)

$(- 2.75, - 10)$

$x = - 2.75$ and $x = - 10$ are the two real distinct solutions for the quadratic equation, which means that $x + 2.75$ and $x + 10$ are the factors of the quadratic equation.

$(x + 2.75) (x + 10) = 0$

Expand $(x + 2.75) (x + 10)$ using the FOIL Method.

Apply the distributive property.

$x (x + 10) + 2.75 (x + 10) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 10 + 2.75 (x + 10) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 10 + 2.75 x + 2.75 \cdot 10 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 10 + 2.75 x + 2.75 \cdot 10 = 0$

Move $10$ to the left of $x$ .

$x^{2} + 10 \cdot x + 2.75 x + 2.75 \cdot 10 = 0$

Multiply $2.75$ by $10$ .

$x^{2} + 10 x + 2.75 x + 27.5 = 0$

Add $10 x$ and $2.75 x$ .

$x^{2} + 12.75 x + 27.5 = 0$

The standard quadratic equation using the given set of solutions ${- 2.75, - 10}$ is $y = x^{2} + 12.75 x + 27.5$ .

$y = x^{2} + 12.75 x + 27.5$

Find the Quadratic Equation (-2.75,-10)

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