Understanding Parabolas

The video tutorial covers the properties of parabolas, focusing on their vertex form and direction based on the coefficient 'a'. It includes examples demonstrating how to find the vertex and direction of a parabola, complete the square to convert to vertex form, determine the Y-intercept and real roots, and derive the equation of a parabola from given values.

What is the vertex of a parabola given by the equation y = a(x - h)^2 + k?

• (k, h)

• (-h, k)

• (-k, h)

• (h, k)

If a parabola opens upwards, what can be said about the value of 'a' in its equation?

• a is negative

• a is equal to zero

• a is greater than zero

• a is less than zero

For the equation y = -3(x + 4)^2 + 5, what is the direction of the parabola?

• Downwards

• Leftwards

• Rightwards

• Upwards

In the equation 3x^2 + 12x - 1, what is the y-intercept?

• 1

• 0

• 12

• -1

How many real roots does the parabola 3x^2 + 12x - 1 have?

• Three

• Two

• One

• None

What is the first step in completing the square for the equation 3x^2 + 12x - 1?

• Multiply by 3

• Subtract 12 from both sides

• Factor out the coefficient of x^2

• Add 1 to both sides

After completing the square, what is the vertex of the parabola 3x^2 + 12x - 1?

• (-2, -13)

• (2, 13)

• (-2, 13)

• (2, -13)

What is the equation of a parabola with vertex (1, -1) and a = 2?

• y = 2(x + 1)^2 + 1

• y = 2(x + 1)^2 - 1

• y = 2(x - 1)^2 - 1

• y = 2(x - 1)^2 + 1

In the equation y = a(x - h)^2 + k, what does 'k' represent?

• The direction of the parabola

• The slope of the parabola

• The y-coordinate of the vertex

• The x-coordinate of the vertex

If a parabola has a vertex at (1, -1) and opens upwards, what can be said about 'a'?

• a is undefined

• a is negative

• a is zero

• a is positive