Fractional Quadratics

Name:

Date:

📚 Part 1: Multiple Choice (choose one)

1. Compared with y = x², the graph of y = (1/2)x² is:

narrower

wider

the same width

opens downward

2. For y = -3/4 x² + 1/2 x - 1, the axis of symmetry is at:

x = -1/3

x = 1/3

x = -2/3

x = 2/3

3. Which coefficient primarily controls the parabola's width (how "wide" or "narrow" it is)?

a (the coefficient of x²)

b (the coefficient of x)

c (the constant)

all three equally

4. What is the y-intercept of y = (1/3)x² + x - 2 ?

1/3

-2

✏️ Part 2: Short Answers & Working

5. For y = (1/3)x² + x - 2, calculate the axis of symmetry and the vertex coordinates. Show your working.

6. For y = -2/5 x² + 3/4 x + 1: state whether the parabola opens up or down and whether it is wider or narrower than y = x². Also write the axis of symmetry (numeric or fractional).

7. Algebraically find the x-intercepts of y = (1/2)x² - x. Show factoring or steps.

8. If only the coefficient a in y = ax² + bx + c is halved (a → a/2) while b and c stay the same, explain two effects this change will have on the parabola (mention width and any effect on the axis/vertex).