Find Three Ordered Pair Solutions f(x)=-2x^2+2.5x+1

$f (x) = - 2 x^{2} + 2.5 x + 1$

Step 1

Write $f (x) = - 2 x^{2} + 2.5 x + 1$ as an equation.

$y = - 2 x^{2} + 2.5 x + 1$

Step 2

Choose any value for $x$ that is in the domain to plug into the equation.

Step 3

Choose $0$ to substitute in for $x$ to find the ordered pair.

Remove parentheses.

$y = - 2 \cdot 0^{2} + 2.5 (0) + 1$

Remove parentheses.

$y = - 2 {(0)}^{2} + 2.5 (0) + 1$

Simplify $- 2 {(0)}^{2} + 2.5 (0) + 1$ .

Simplify each term.

Raising $0$ to any positive power yields $0$ .

$y = - 2 \cdot 0 + 2.5 (0) + 1$

Multiply $- 2$ by $0$ .

$y = 0 + 2.5 (0) + 1$

Multiply $2.5$ by $0$ .

$y = 0 + 0 + 1$

Simplify by adding numbers.

Add $0$ and $0$ .

$y = 0 + 1$

Add $0$ and $1$ .

$y = 1$

Use the $x$ and $y$ values to form the ordered pair.

$(0, 1)$

Step 4

Choose $1$ to substitute in for $x$ to find the ordered pair.

Remove parentheses.

$y = - 2 \cdot 1^{2} + 2.5 (1) + 1$

Remove parentheses.

$y = - 2 {(1)}^{2} + 2.5 (1) + 1$

Simplify $- 2 {(1)}^{2} + 2.5 (1) + 1$ .

Simplify each term.

One to any power is one.

$y = - 2 \cdot 1 + 2.5 (1) + 1$

Multiply $- 2$ by $1$ .

$y = - 2 + 2.5 (1) + 1$

Multiply $2.5$ by $1$ .

$y = - 2 + 2.5 + 1$

Simplify by adding numbers.

Add $- 2$ and $2.5$ .

$y = 0.5 + 1$

Add $0.5$ and $1$ .

$y = 1.5$

Use the $x$ and $y$ values to form the ordered pair.

$(1, 1.5)$

Step 5

Choose $2$ to substitute in for $x$ to find the ordered pair.

Remove parentheses.

$y = - 2 \cdot 2^{2} + 2.5 (2) + 1$

Remove parentheses.

$y = - 2 {(2)}^{2} + 2.5 (2) + 1$

Simplify $- 2 {(2)}^{2} + 2.5 (2) + 1$ .

Simplify each term.

Raise $2$ to the power of $2$ .

$y = - 2 \cdot 4 + 2.5 (2) + 1$

Multiply $- 2$ by $4$ .

$y = - 8 + 2.5 (2) + 1$

Multiply $2.5$ by $2$ .

$y = - 8 + 5 + 1$

Simplify by adding numbers.

Add $- 8$ and $5$ .

$y = - 3 + 1$

Add $- 3$ and $1$ .

$y = - 2$

Use the $x$ and $y$ values to form the ordered pair.

$(2, - 2)$

Step 6

These are three possible solutions to the equation.

$(0, 1), (1, 1.5), (2, - 2)$

Step 7

Find Three Ordered Pair Solutions f(x)=-2x^2+2.5x+1

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