Question

Assuming all parabolas are of the form y=ax^(2)+bx+c, drag and drop the grap to match the appropriate a-value. a=-4,a=-0.25,a=0.25

Answer 1

Match the value of 'a' to the appropriate graph by looking at the parabola's direction and width: 'a=-4' for a narrow, downward-opening parabola, 'a=-0.25' for a wide, downward-opening parabola, and 'a=0.25' for a wide, upward-opening parabola.

Step-by-step explanation:

The student's question involves matching given values of 'a' in the parabolic equation y=ax^2+bx+c to the appropriate graph. The value of 'a' determines the parabola's direction of opening and its wideness. For instance, if a is negative, the parabola opens downwards; if a is positive, it opens upwards. A larger absolute value of 'a' means the parabola is narrower, while a smaller absolute value means it's wider.

There are three given a-values: a=-4, a=-0.25, and a=0.25. When a=-4, the parabola opens downwards and is relatively narrow due to the largeness of the absolute value of 'a'. When a=-0.25, the parabola still opens downwards but is much wider. Lastly, when a=0.25, the parabola opens upwards and is wide as well because of the small absolute value of 'a'. Therefore, the student should match each graph with these parabola characteristics based on their understanding of how 'a' affects the shape.