Determine if the parabola opens up or down.
$y=\frac{1}{2}{x}^2-5x$

• A. Up
• B. Down
• C. To the left
• D. To the right

Answer: (A)

Verified step by step guidance

1. Identify the quadratic function given: \(y=\frac{1}{2}x^{2} - 5x\).
2. Recall that the general form of a quadratic function is \(y = ax^{2} + bx + c\), where \(a\), \(b\), and \(c\) are constants.
3. Focus on the coefficient \(a\) of the \(x^{2}\) term, which determines the direction the parabola opens.
4. Since \(a = \frac{1}{2}\) is positive, the parabola opens upward.
5. If \(a\) were negative, the parabola would open downward; the parabola never opens to the left or right in this form.