Understanding Parabolas and Quadratics

This video tutorial explains the key features of parabolas, focusing on how coefficients affect their graphs. It covers graphing parabolas by finding zeros and vertices, comparing parabolas with different coefficients, and using formulas to find the axis of symmetry. An example problem is solved to illustrate these concepts.

What determines if a parabola opens upwards or downwards?

• The sum of the coefficients

• The sign of the coefficient of x

• The sign of the coefficient of x^2

• The value of the constant term

How do you find the zeros of a quadratic equation?

• By setting the equation to zero and solving for x

• By finding the vertex

• By comparing it to the parent function

• By calculating the axis of symmetry

What is the vertex of the parabola y = 2x^2 + 4x - 6?

• (-3, 0)

• (0, -6)

• (1, -6)

• (-1, -8)

How does the coefficient of x^2 affect the width of a parabola?

• A larger coefficient makes the parabola wider

• A smaller coefficient makes the parabola narrower

• A coefficient greater than 1 makes the parabola narrower

• A coefficient less than 1 makes the parabola narrower

What happens to the graph of y = x^2 when it becomes y = -x^2?

• It shifts to the right

• It opens downwards

• It becomes wider

• It becomes narrower

Which formula can be used to find the axis of symmetry?

• x = a / 2b

• x = -b / 2a

• x = b / 2a

• x = -a / 2b

What is the axis of symmetry for the equation y = 2x^2 + 4x - 6?

• x = 2

• x = 0

• x = -1

• x = 1

In the equation y = -1/2x^2 + 4x - 6, what does the negative sign indicate?

• The parabola opens upwards

• The parabola opens downwards

• The parabola is narrower

• The parabola is wider

What are the zeros of the equation y = -1/2x^2 + 4x - 6?

• x = 2 and x = 6

• x = -2 and x = -6

• x = 0 and x = 4

• x = 1 and x = 3

What is the vertex of the parabola y = -1/2x^2 + 4x - 6?

• (6, 0)

• (2, 4)

• (4, 2)

• (0, -6)