Vertex Form of Quadratic Equations
This worksheet focuses on understanding and working with the vertex form of quadratic equations, including identifying the vertex, axis of symmetry, and graphing parabolas.
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Vertex Form of Quadratic Equations
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
For a quadratic equation in vertex form, y = a(x - h)² + k, the vertex is at the point ( , ).
1. Identify the vertex of the parabola represented by the equation y = 2(x - 3)² + 1. Vertex: ( , ).
2. Identify the vertex of the parabola represented by the equation y = -(x + 5)² - 4. Vertex: ( , ).
3. Identify the vertex of the parabola represented by the equation y = 0.5x² + 7. Vertex: ( , ).
4. Which of the following equations is in vertex form?
y = x² + 3x - 2
y = (x - 4)² + 5
y = 2(x + 1)(x - 3)
y = 5x + 8
5. What is the axis of symmetry for the parabola y = -3(x + 2)² - 7?
x = 2
x = -2
y = -7
y = 7
6. For the quadratic equation y = (x - 1)² - 3:
a) Identify the vertex:
b) Identify the axis of symmetry:
c) Does the parabola open upwards or downwards? Explain.
7. Write a quadratic equation in vertex form for a parabola with a vertex at (-2, 5) that opens downwards.
8. The 'a' value in y = a(x - h)² + k determines the width of the parabola.
True
False
9. If 'a' is positive in the vertex form, the parabola opens upwards.
True
False
10. A projectile's height (in meters) is given by the equation h(t) = -5(t - 3)² + 45, where t is the time in seconds.
a) What is the maximum height the projectile reaches?
b) At what time does the projectile reach its maximum height?
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