Example 1
Completion requirements
| Example 1 |
Multimedia |
The equations \(y = -(x - 2)^2 + 5\) and \(y = -x + 5\) form a system. Solve the system graphically, and verify the solution using substitution.
Graph the system and determine any points of intersection.
The points of intersection are \((1, 4)\) and \((4, 1)\), so these are the solutions to the system.
To verify a solution, the values must be substituted into each equation.
Verify for \((1, 4)\).
Verify for \((4, 1)\).
The points of intersection are \((1, 4)\) and \((4, 1)\), so these are the solutions to the system.
The solutions can be verified by substituting them into the original equations.
To verify a solution, the values must be substituted into each equation.
Verify for \((1, 4)\).
\(y = -(x - 2)^2 + 5\)
| Left Side | Right Side |
|---|---|
|
\[\begin{array}{r}
y \\ 4 \end{array}\] |
\[\begin{array}{l}
- \left( {x - 2} \right)^2 + 5 \\ - \left( {1 - 2} \right)^2 + 5 \\ 4 \end{array}\] |
| LS = RS | |
\(y = -x + 5\)
| Left Side | Right Side |
|---|---|
|
\[\begin{array}{r}
y \\ 4 \end{array}\] |
\[\begin{array}{l}
- x + 5 \\ - 1 + 5 \\ 4 \end{array}\] |
| LS = RS | |
Verify for \((4, 1)\).
\(y = -(x - 2)^2 + 5\)
| Left Side | Right Side |
|---|---|
|
\[\begin{array}{r}
y \\ 1 \end{array}\] |
\[\begin{array}{l}
- \left( {x - 2} \right)^2 + 5 \\ - \left( {4 - 2} \right)^2 + 5 \\ 1 \end{array}\] |
| LS = RS | |
\(y = -x + 5\)
| Left Side | Right Side |
|---|---|
|
\[\begin{array}{r}
y \\ 1 \end{array}\] |
\[\begin{array}{l}
- x + 5 \\ - 4 + 5 \\ 1 \end{array}\] |
| LS = RS | |