Example 1
Completion requirements
| Example 1 |
Determine the zeros of the factored quadratic function \(f(x) = 2(x + 5)(3x - 2)\).
To find the zeros, determine what values of \(x\) will cause at least one of the factors to equal zero. In order for the function to be equal to zero, either \((x + 5)\) or \((3x - 2)\) must be equal to zero.
Therefore,
This means that the zeros of the function \(f(x) = 2(x + 5)(3x - 2)\) are \(x = -5\) and \(x = \frac{2}{3}\). And, as such, the \(x\)-intercepts of the graph of \(f(x) = 2(x + 5)(3x - 2)\) are \(x = -5\) and \(x = \frac{2}{3}\).
Therefore,
\(\begin{align}
x + 5 &= 0 \\
x &= -5 \end{align}\)
x + 5 &= 0 \\
x &= -5 \end{align}\)
or
\(\begin{align}
3x - 2 &= 0 \\
3x &= 2 \\
x &= \frac{2}{3}
\end{align}\)
3x - 2 &= 0 \\
3x &= 2 \\
x &= \frac{2}{3}
\end{align}\)
This means that the zeros of the function \(f(x) = 2(x + 5)(3x - 2)\) are \(x = -5\) and \(x = \frac{2}{3}\). And, as such, the \(x\)-intercepts of the graph of \(f(x) = 2(x + 5)(3x - 2)\) are \(x = -5\) and \(x = \frac{2}{3}\).