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Graphing Fractional Quadratics
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Graphing Fractional Quadratics
📚 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
0
4. Which formula gives the axis of symmetry of y = ax2 + bx + c?
x = b/(2a)
x = −b/(2a)
x = −c/b
✏️ Part 2: Short Answers & Graphing Tasks
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.
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