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.

Grade 9 Math AlgebraVertex Form

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Includes

Fill in the BlanksMultiple Choice2 Short AnswerTrue / False

Standards

CCSS.MATH.CONTENT.HSA.SSE.B.3.ACCSS.MATH.CONTENT.HSA.CED.A.2

Topics

AlgebraVertex FormQuadratic EquationsParabola

7 sections · Free to use · Printable

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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?