Understanding the Key Features of a Parabola

This video tutorial explains the key features of a parabola, focusing on how coefficients affect its graph. It covers graphing parabolas by finding zeros and the vertex, comparing different coefficients with the parent function, and determining the axis of symmetry using various methods. An example problem is solved to illustrate these concepts, emphasizing the impact of negative coefficients on the graph's orientation and width.

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

• x = 1 and x = -3

• x = 2 and x = -2

• x = 3 and x = -1

• x = 0 and x = -4

How does the graph of y = 2x^2 compare to the parent function y = x^2?

• It is the same width

• It is narrower

• It is wider

• It opens downwards

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

• x = 2

• x = 1

• x = -1

• x = 0

Which formula can be used to find the axis of symmetry in a quadratic equation?

• x = -a/2b

• x = -b/2a

• x = b/2a

• x = a/2b

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

• x = 6 and x = 2

• x = 5 and x = 3

• x = 3 and x = 1

• x = 4 and x = 0

How does the negative sign in front of y = -1/2x^2 affect the graph?

• It makes the graph open upwards

• It makes the graph open downwards

• It makes the graph wider

• It makes the graph narrower

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

• (4, 2)

• (0, 6)

• (2, 4)

• (6, 0)