Vertex Form of Quadratic Equations

Vertex Form of Quadratic Equations

Read each question carefully and provide clear, concise answers. Show all your work for full credit.

1. What is the vertex of the quadratic function y = 2(x - 3)² + 4?

2. In the vertex form equation y = a(x - h)² + k, the value of 'a' determines the   and   of the parabola.

3. To convert a quadratic equation from standard form (y = ax² + bx + c) to vertex form, you can use the method of  .

4. Write the equation of a parabola with a vertex at (-1, 5) that opens downwards and is wider than y = x².

5. Explain how the sign of 'a' in vertex form affects the graph of the parabola.

6. Graph the quadratic function y = -(x + 2)² + 1 on the coordinate plane below. Label the vertex and at least two other points.

7. The axis of symmetry for a parabola in vertex form y = a(x - h)² + k is always x = h.

8. A ball is thrown upwards from a height of 5 feet with an initial velocity of 48 feet per second. The height of the ball (h) after t seconds can be modeled by the equation h(t) = -16t² + 48t + 5. Convert this equation to vertex form and determine the maximum height the ball reaches and the time it takes to reach that height.