Find the Quadratic Equation (7,1)

$(7, 1)$

$x = 7$ and $x = 1$ are the two real distinct solutions for the quadratic equation, which means that $x - 7$ and $x - 1$ are the factors of the quadratic equation.

$(x - 7) (x - 1) = 0$

Expand $(x - 7) (x - 1)$ using the FOIL Method.

Apply the distributive property.

$x (x - 1) - 7 (x - 1) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 1 - 7 (x - 1) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 1 - 7 x - 7 \cdot - 1 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 1 - 7 x - 7 \cdot - 1 = 0$

Move $- 1$ to the left of $x$ .

$x^{2} - 1 \cdot x - 7 x - 7 \cdot - 1 = 0$

Rewrite $- 1 x$ as $- x$ .

$x^{2} - x - 7 x - 7 \cdot - 1 = 0$

Multiply $- 7$ by $- 1$ .

$x^{2} - x - 7 x + 7 = 0$

Subtract $7 x$ from $- x$ .

$x^{2} - 8 x + 7 = 0$

The standard quadratic equation using the given set of solutions ${7, 1}$ is $y = x^{2} - 8 x + 7$ .

$y = x^{2} - 8 x + 7$

Find the Quadratic Equation (7,1)

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