Exploring Quadratic Functions

What is the vertex of the quadratic function y = 2x^2 - 4x + 1?

• (0, 1)

• (2, 3)

• (1, 0)

• (1, -1)

Determine the maximum or minimum value of the function y = -3x^2 + 6x - 2.

• 1

• -1

• 0

• 2

Explain the axis of symmetry for the quadratic function y = x^2 + 4x + 4.

• x = 2

• x = -4

• x = -2

• x = 0

How do you find the vertex of a quadratic function in standard form?

• The vertex is at ( -b/(2a), f(-b/(2a)) ).

• The vertex is at (b/a, 0).

• The vertex is at (0, 0).

• The vertex is at (a, -b).

For the function y = x^2 - 2x + 5, is there a maximum or minimum?

• Maximum

• Minimum

• No extrema

• Undefined

What is the significance of the coefficient 'a' in the quadratic equation y = ax^2 + bx + c?

• The coefficient 'a' determines the number of roots of the equation.

• The coefficient 'a' determines the direction and width of the parabola.

• The coefficient 'a' affects the position of the vertex only.

• The coefficient 'a' indicates the color of the parabola.

Identify the vertex of the quadratic function y = -x^2 + 2x + 3.

• (1, 2)

• (1, 4)

• (0, 3)

• (2, 1)

How does the symmetry of a parabola relate to its vertex?

• The vertex is located at the origin of the parabola.

• The vertex is the axis of symmetry for a parabola.

• The vertex is the highest point of the parabola.

• The vertex determines the width of the parabola.

Calculate the vertex of the function y = 3x^2 + 12x + 9 using the formula.

• (-1, 0)

• (1, 6)

• (-2, -3)

• (0, 9)

What is the effect of changing the value of 'c' in the quadratic function y = ax^2 + bx + c on its graph?

• The value of 'c' affects the vertical position of the graph.

• The value of 'c' determines the slope of the graph.

• The value of 'c' changes the width of the graph.

• The value of 'c' affects the color of the graph.