Find the Quadratic Equation (1,4)

$(1, 4)$

Step 1

$x = 1$ and $x = 4$ are the two real distinct solutions for the quadratic equation, which means that $x - 1$ and $x - 4$ are the factors of the quadratic equation.

$(x - 1) (x - 4) = 0$

Step 2

Expand $(x - 1) (x - 4)$ using the FOIL Method.

Apply the distributive property.

$x (x - 4) - 1 (x - 4) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 4 - 1 (x - 4) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 4 - 1 x - 1 \cdot - 4 = 0$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 4 - 1 x - 1 \cdot - 4 = 0$

Move $- 4$ to the left of $x$ .

$x^{2} - 4 \cdot x - 1 x - 1 \cdot - 4 = 0$

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

$x^{2} - 4 x - x - 1 \cdot - 4 = 0$

Multiply $- 1$ by $- 4$ .

$x^{2} - 4 x - x + 4 = 0$

Subtract $x$ from $- 4 x$ .

$x^{2} - 5 x + 4 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${1, 4}$ is $y = x^{2} - 5 x + 4$ .

$y = x^{2} - 5 x + 4$

Step 5

Find the Quadratic Equation (1,4)

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