Quadratic Function: Graphing Parabolas

What is the general form of a quadratic function?

• f(x) = ax^2 + bx + c

• f(x) = ax^2 + bx + d

• f(x) = ax^2 + c

• f(x) = ax^2 + bx

How many x-intercepts can a parabola have?

• 1

• 0

• 2

• 3

What is the vertex form of a quadratic function?

• y = a(x - h)^2 - k

• y = a(x + h)^2 + k

• y = a(x + h)^2 - k

• y = a(x - h)^2 + k

Explain how to find the axis of symmetry of a parabola.

• x = a / (2b)

• x = -a / (2b)

• x = b / (2a)

• x = -b / (2a)

What does the 'a' value in a quadratic function determine about the parabola?

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

• The 'a' value determines the vertex of the parabola.

• The 'a' value determines the x-intercepts of the parabola.

• The 'a' value determines the axis of symmetry of the parabola.

Describe the shape of the graph of a quadratic function with a positive 'a' value.

• Spiral

• Straight line

• V-shape

• U-shape

How can you determine if a parabola opens upwards or downwards by looking at the quadratic function?

• Check the value of the constant term in the function

• Count the number of x-intercepts

• Look at the y-intercept of the function

• Determine the sign of the coefficient of the x^2 term.

What is the significance of the 'h' value in the vertex form of a quadratic function?

• The 'h' value represents the horizontal shift of the parabola.

• The 'h' value determines the vertical stretch of the parabola.

• The 'h' value represents the axis of symmetry of the parabola.

• The 'h' value indicates the y-intercept of the parabola.

Explain how to find the vertex of a parabola given a quadratic function in standard form.

• The vertex can be found by taking the square root of the discriminant

• The vertex of the parabola can be found by calculating x = -b / (2a) and then substituting this x-value back into the original function to find the y-coordinate.

• The vertex is located at the y-intercept of the parabola

• The vertex is always at (0,0) for any parabola

What is the role of the 'c' value in the vertex form of a quadratic function?

• Vertical shift or translation of the parabola

• Determines the concavity of the parabola

• Affects the axis of symmetry of the parabola

• Controls the horizontal shift of the parabola