Graphing Fractional Quadratics

Name:

Date:

📚 Part 1: Multiple Choice

1. Which parabola is wider than y = x²?

y = 2x²

y = (1/2)x²

y = -3x²

2. Which value of a makes a parabola open downwards?

a = 1/3

a = 0

a = -1/2

3. For y = (1/3)x² + x − 2, the y‑intercept is:

1/3

−2

4. Which formula gives the axis of symmetry of y = ax² + bx + c?

x = b/(2a)

x = −b/(2a)

x = −c/b

5. Identify a, b and c for y = (1/2)x² − (3/4)x + 1.

6. Using the formula for the vertex x = −b/(2a), find the vertex of y = (1/2)x² + x − 2. Show working.

7. Use a graphing calculator or software to graph y = −(2/5)x² + (3/4)x + 1. Record:

a) Axis of symmetry: _________

b) Vertex (give coordinates): _________

c) Approximate x‑intercepts: _________ and _________

8. In one sentence, describe how a fractional 0 < a < 1 affects the parabola compared with a = 1.

9. Graph activity (use technology): For y = (5/6)x² − (1/2)x, sketch the parabola in the box and write the vertex and y‑intercept.

Vertex: _________ y‑intercept: _________

10. Compare y = x² and y = (1/3)x². List two observable differences from the graphs.