Question

Determine whether the graph of the quadratic function y = –3x2 + 2x + 5 opens upward or downward. Explain.

Answer 1

The graph of the function opens downwards.

Step-by-step explanation:

The graph opens upward if the coefficient of x^2 is higher than 0.

But, the coefficient of x^2 (-3) is less than 0.

So the graph of the function opens downwards.

Answer 2

The graph of the quadratic function y = -3x² + 2x + 5 opens downward because the coefficient of the x² term is negative.

Step-by-step explanation:

To determine whether the graph of the quadratic function y = –3x² + 2x + 5 opens upward or downward, we need to analyze the function’s leading coefficient, constant term, and the relationship between these terms.

The leading coefficient of a quadratic function is the coefficient of the x² term, which in this case is –3. If the leading coefficient is positive, the graph opens upward, while if it is negative, the graph opens downward.

The constant term of a quadratic function is the term without any variable, which in this case is 5. The constant term affects the vertical position of the graph, with a positive constant term resulting in an upward shift and a negative constant term resulting in a downward shift.

In this function, the leading coefficient is negative, which means the graph opens downward. However, the constant term is positive, which shifts the graph upward. The graph of the quadratic function y = –3x² + 2x + 5 opens downward.