Question

"In the standard form equation for a quadratic function, f(x) = ax² + bx + C, what does the parameter ""a"" determine or represent?

a. It is the input to the function.
b. It is the scalar and determines if the graph of the parabola points left or right.
c. It determines the location of the vertex of the function.
d. It is the scalar and determines if the graph of the parabola points up or down.

Answer 1

The parameter 'a' in a quadratic function determines the orientation of the parabola (upwards if positive, downwards if negative) as well as the width of the parabola.

Step-by-step explanation:

In the standard form of a quadratic function f(x) = ax² + bx + c, the parameter 'a' is significant as it determines the orientation and width of the graph of the parabola. If 'a' is positive, the graph opens upwards, and if 'a' is negative, the graph opens downwards. The absolute value of 'a' affects how wide or narrow the parabola is; smaller absolute values result in wider parabolas, while larger absolute values lead to narrower parabolas. This means that the correct answer to the question is 'd. It is the scalar and determines if the graph of the parabola points up or down.'