Understanding Parabolas

The video tutorial introduces parabolas, explaining their standard form and how to graph them using a calculator. It covers the concepts of the axis of symmetry and the vertex, detailing how to find these using formulas. The tutorial includes examples to practice finding the axis of symmetry and vertex, emphasizing the significance of the vertex as a minimum or maximum point. The session concludes with a summary of key points and an invitation for further questions.

What is the standard form of a quadratic equation?

• y = ax + b

• y = ax^2 + bx + c

• y = ax^3 + bx^2 + c

• y = a + bx + c

What shape does the graph of a quadratic equation represent?

• A circle

• A straight line

• A U-shaped curve

• A zigzag line

If the coefficient 'a' in a quadratic equation is positive, how does the parabola open?

• It does not open

• Sideways

• Upwards

• Downwards

What is the formula for the axis of symmetry in a quadratic equation?

• x = -a / 2b

• x = b / 2a

• x = -b / 2a

• x = a / 2b

What is the vertex of a parabola?

• The highest or lowest point on the graph

• The midpoint of the graph

• The intersection with the y-axis

• The intersection with the x-axis

In the equation y = x^2 + 8x + 15, what is the axis of symmetry?

• x = -8

• x = 4

• x = -4

• x = 8

For the equation y = -x^2 + 10x - 23, what is the vertex?

• (5, 2)

• (-5, 2)

• (5, -2)

• (-5, -2)

If the coefficient 'a' is negative, how does the parabola open?

• Upwards

• It does not open

• Sideways

• Downwards

In the equation y = -2x^2 + 4x, what is the axis of symmetry?

• x = 1

• x = -2

• x = -1

• x = 2

For the equation y = -2x^2 + 4x, what is the vertex?

• (2, 4)

• (2, -4)

• (1, 4)

• (1, -4)