Question

Describe how the values of a and k affect the graphical and tabular representations of the functions y=ax^2, y=x^2+k, and y=ax^2+k.

a. Changing the parabola's width and direction, shifting it vertically
b. Shifting the parabola horizontally and vertically, no effect on width
c. Only changing the parabola's width, no effect on position
d. Altering the parabola's position and width simultaneously

Answer 1

The values of 'a' and 'k' in quadratic functions y = ax^2, y = x^2 + k, and y = ax^2 + k affect the graphical and tabular representations in different ways. 'a' changes the width and direction of the parabola, while 'k' shifts the parabola vertically without affecting its width.

Step-by-step explanation:

a. The value of 'a' in the function y = ax^2 affects the width and direction of the parabola. If 'a' is positive, the parabola opens upwards, and if 'a' is negative, the parabola opens downwards. Increasing the absolute value of 'a' makes the parabola narrower (increases the width).

b. The value of 'k' in the function y = x^2 + k shifts the parabola vertically. If 'k' is positive, the parabola moves upward, and if 'k' is negative, the parabola moves downward. Changing 'k' does not affect the width of the parabola.

c. Similar to (a), changing the value of 'a' in the function y = ax^2 + k affects the width and direction of the parabola. Changing 'k' shifts the parabola vertically without affecting its width.

d. In the function y = ax^2 + k, altering both 'a' and 'k' simultaneously will cause a combined effect of changing the width, direction, and position of the parabola.