Question

Assuming all parabolas are of the form y, equals, a, x, squared, plus, b, x, plus, cy=ax 2 +bx+c, drag and drop the graphs to match the appropriate a-value (if necessary). a, equals, minus, 0, point, 2, 5a=−0.25 a, equals, minus, 4a=−4 a, equals, minus, 1a=−1

Answer 1

Left graph: a = 1 (standard upward parabola). Middle graph: a = 0.25 (flattened upward parabola). Right graph: a = -1 (downward parabola).

The provided a-values are a = 1, a = 0.25, and a = -1. Let's analyze each one step by step:

1. a = 1:

For a = 1, the parabola is of the form
`\(y = x^2 + bx + c\)`. This represents a standard upward-opening parabola.

2. a = 0.25:

For a = 0.25, the parabola is
`\(y = 0.25x^2 + bx + c\)`. The positive, smaller magnitude of a flattens the parabola slightly compared to the standard form.

3. a = -1:

For a = -1, the parabola is
`y = -x^2 + bx + c`. The negative sign of a causes the parabola to open downward.

Therefore, the correct association is:

- Leftmost graph: a = 1

- Middle graph: a = 0.25

- Rightmost graph: a = -1

This step-by-step calculation explains the impact of each a-value on the form and orientation of the parabolic graphs.