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Quadratic Functions Mastery
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Quadratic Functions Mastery
Worksheet 1 — 📚 Part 1: Multiple Choice
1. Which equation represents a parabola with vertex (2, -3) that opens upward?
y = (x - 2)^2 - 3
y = -2(x - 2)^2 - 3
y = (x + 2)^2 + 3
2. What is the axis of symmetry for y = -2x^2 + 8x - 5?
x = -2
x = 2
x = 4
3. Check all true statements about y = (x - 1)^2 + 4:
Vertex (1, 4)
Opens downward
Axis of symmetry x = 1
y-intercept = 5
Worksheet 1 — ✏️ Part 2: Short Answers / Work
4. Find the vertex and axis of symmetry for y = 3x^2 - 12x + 11. Show work.
5. Solve by factoring: x^2 - 5x + 6 = 0. Write the factorization and solutions.
6. Convert to vertex form and state the vertex: y = x^2 - 4x + 3.
Quadratic Functions Mastery
Worksheet 2 — 📚 Part 1: Multiple Choice
1. Solve by factoring: x^2 + x - 6 = 0. Which pair of solutions is correct?
x = -3, 2
x = 3, -2
x = 1, -6
2. The discriminant of 2x^2 + 3x + 1 is 1. What does this tell you?
One real repeated root
Two distinct real rational roots
No real roots
3. What is the vertex of y = -1/2(x + 4)^2 + 7?
(-4, 7)
(4, -7)
(-7, 4)
4. Check all true for y = -x^2 + 4x - 3:
Opens down
Vertex x-coordinate = 2
y-intercept = -3
Axis of symmetry y = 2
Worksheet 2 — ✏️ Part 2: Short Answers / Application
5. Factor and state the x-intercepts: y = 2x^2 - 8x.
6. Complete the square to write vertex form and give the vertex: y = x^2 + 6x + 5.
7. A ball follows the path y = -16t^2 + 32t + 5 (y in feet, t in seconds). Estimate when the ball first hits the ground (y = 0). Show the equation you solve.
Quadratic Functions Mastery
Worksheet 3 — 📚 Part 1: Multiple Choice
1. Which change makes the parabola y = x^2 wider?
y = 3x^2
y = (1/2)x^2
y = -2x^2
2. What is the vertex of y = -3x^2 + 12x - 9?
(2, 3)
(2, -3)
(-2, 3)
3. Solve: x^2 - 9 = 0
x = 0, ±9
x = -3, 3
x = 9, -9
Worksheet 3 — ✏️ Part 2: Short Answers / Concept
4. For y = -2(x - 1)^2 + 8, state: vertex, axis of symmetry, direction (up/down), and y-intercept. Show quick calculations.
5. Solve by factoring: 3x^2 - 12x + 9 = 0. Show steps.
6. In one or two sentences, explain why x = -b/(2a) gives the x-coordinate of the vertex for y = ax^2 + bx + c.
Quadratic Functions Mastery
Worksheet 4 — 📚 Part 1: Multiple Choice
1. Which quadratic has zeros at x = 1 and x = 4?
y = x^2 - 5x + 4
y = x^2 + 5x + 4
y = x^2 - 3x - 4
2. A negative discriminant indicates:
Two distinct real roots
One real repeated root
No real roots (two complex)
3. For y = (x - 3)^2 - 16, the vertex is and the minimum value is:
(3, -16), min = -16
(3, 16), min = 16
(-3, -16), min = -16
Worksheet 4 — ✏️ Part 2: Matching & Short Response
4. Match each equation (left) with its vertex or property (right). Draw lines between columns.
A. y = (x - 2)^2 - 3
B. y = - (x + 1)^2 + 4
C. y = x^2 + 4x + 3
D. y = 2(x - 0)^2
1. vertex (2, -3)
2. opens down, vertex (-1, 4)
3. factors to (x+1)(x+3), zeros -1, -3
4. narrower than y = x^2, vertex (0,0)
5. Solve: x^2 + 2x - 15 = 0 by factoring. State solutions.
6. Sketch a parabola with vertex (-1, 2) and opening down. Label vertex and axis. (Use the box below.)
Quadratic Functions Mastery
Worksheet 5 — 📚 Part 1: Multiple Choice
1. If f(x) = x^2, what transformation gives g(x) = f(x - 2) + 5?
Shift right 2 and up 5
Shift left 2 and up 5
Reflect across x-axis then shift up 5
2. Which equation has vertex (0, -4) and opens upward?
y = x^2 - 4
y = -(x)^2 - 4
y = (x + 4)^2
3. The quadratic x^2 - 4x + 4 has:
Two distinct real roots
One real repeated root
No real roots
4. Check all true for a parabola with a > 0:
Opens up
Vertex is a minimum
Always has two real roots
Worksheet 5 — ✏️ Part 2: Short Answers / Modeling
5. Convert to vertex form and identify the vertex: y = 2x^2 - 8x + 6. Show steps.
6. Solve by factoring: 4x^2 - 12x + 9 = 0. Show factorization and solution(s).
7. A parabola has vertex (1, -2) and passes through (2, 0). Find its equation in vertex form.
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