Linear Algebra Examples

$y - 0.25 {(x - 6.5)}^{2} - 20$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(x - 6.5)}^{2}$ as $(x - 6.5) (x - 6.5)$ .

$y - 0.25 ((x - 6.5) (x - 6.5)) - 20$

Step 1.2

Expand $(x - 6.5) (x - 6.5)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$y - 0.25 (x (x - 6.5) - 6.5 (x - 6.5)) - 20$

Step 1.2.2

Apply the distributive property.

$y - 0.25 (x \cdot x + x \cdot - 6.5 - 6.5 (x - 6.5)) - 20$

Step 1.2.3

Apply the distributive property.

$y - 0.25 (x \cdot x + x \cdot - 6.5 - 6.5 x - 6.5 \cdot - 6.5) - 20$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $x$ by $x$ .

$y - 0.25 (x^{2} + x \cdot - 6.5 - 6.5 x - 6.5 \cdot - 6.5) - 20$

Step 1.3.1.2

Move $- 6.5$ to the left of $x$ .

$y - 0.25 (x^{2} - 6.5 \cdot x - 6.5 x - 6.5 \cdot - 6.5) - 20$

Step 1.3.1.3

Multiply $- 6.5$ by $- 6.5$ .

$y - 0.25 (x^{2} - 6.5 x - 6.5 x + 42.25) - 20$

Step 1.3.2

Subtract $6.5 x$ from $- 6.5 x$ .

$y - 0.25 (x^{2} - 13 x + 42.25) - 20$

Step 1.4

Apply the distributive property.

$y - 0.25 x^{2} - 0.25 (- 13 x) - 0.25 \cdot 42.25 - 20$

Step 1.5

Simplify.

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Step 1.5.1

Multiply $- 13$ by $- 0.25$ .

$y - 0.25 x^{2} + 3.25 x - 0.25 \cdot 42.25 - 20$

Step 1.5.2

Multiply $- 0.25$ by $42.25$ .

$y - 0.25 x^{2} + 3.25 x - 10.5625 - 20$

Step 2

Subtract $20$ from $- 10.5625$ .

$y - 0.25 x^{2} + 3.25 x - 30.5625$