Problem 53 - College Algebra

Question

Explain how to decide whether a parabola opens upward or downward.

Step-by-Step Solution

Answer

The parabola opens upward if 'a' (the coefficient of the quadratic term in the parabola's equation) is positive and opens downward if 'a' is negative.

Step 1: Identify the quadratic term and its coefficient

From the equation of the parabola in standard form \(y = ax^2 + bx + c\), identify 'a' which is the coefficient of the quadratic term (the term with \(x^2\)).

Step 2: Determine the sign of the coefficient

After identifying 'a', determine its sign. If 'a' is positive (greater than zero), the parabola opens upward. If 'a' is negative (less than zero), the parabola opens downward.

Step 3: Make the final decision

Based on the sign of 'a', make your final decision. If 'a' > 0, say 'The parabola opens upward'. If 'a' < 0, say 'The parabola opens downward'.