Find the Quadratic Equation 1 , 13

$1$ , $13$

Step 1

$x = 1$ and $x = 13$ are the two real distinct solutions for the quadratic equation, which means that $x - 1$ and $x - 13$ are the factors of the quadratic equation.

$(x - 1) (x - 13) = 0$

Step 2

Expand $(x - 1) (x - 13)$ using the FOIL Method.

Apply the distributive property.

$x (x - 13) - 1 (x - 13) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 13 - 1 (x - 13) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 13 - 1 x - 1 \cdot - 13 = 0$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 13 - 1 x - 1 \cdot - 13 = 0$

Move $- 13$ to the left of $x$ .

$x^{2} - 13 \cdot x - 1 x - 1 \cdot - 13 = 0$

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

$x^{2} - 13 x - x - 1 \cdot - 13 = 0$

Multiply $- 1$ by $- 13$ .

$x^{2} - 13 x - x + 13 = 0$

Subtract $x$ from $- 13 x$ .

$x^{2} - 14 x + 13 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${1, 13}$ is $y = x^{2} - 14 x + 13$ .

$y = x^{2} - 14 x + 13$

Step 5

Find the Quadratic Equation 1 , 13

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