Understanding Parabolas in Standard Form

The video tutorial explains how to write equations of parabolas in standard and vertex forms. It covers factoring and completing the square to transform equations, and discusses graphing parabolas, identifying the vertex, and determining the direction of opening. Two examples are provided: one with x squared and another with y squared, illustrating the process of rewriting equations and analyzing their graphs.

What is the standard form of a parabola as described in the textbook?

• y = a(x - h)^2 + k

• x = a(y - k)^2 + h

• None of the above

• Both A and B

What is the first step in converting an equation with x squared into standard form?

• Multiply by a constant

• Complete the square

• Factor out the leading coefficient

• Add a constant to both sides

When completing the square for x^2 + 6x, what value is added inside the parentheses?

• 12

• 9

• 6

• 18

What does a negative 'a' value indicate about the direction a parabola opens?

• Opens to the right

• Opens to the left

• Opens downwards

• Opens upwards

What is the vertex of the parabola y = -2(x + 3)^2 + 34?

• (-34, 3)

• (34, -3)

• (3, -34)

• (-3, 34)

In converting an equation with y squared, what is the first step?

• Multiply by a constant

• Complete the square

• Factor out the leading coefficient

• Add a constant to both sides

What is the result of factoring y^2 - 8y + 16?

• (y + 8)(y - 2)

• (y - 8)(y + 2)

• (y + 4)(y + 4)

• (y - 4)(y - 4)

What does a positive 'a' value indicate about the direction a parabola opens?

• Opens to the left

• Opens to the right

• Opens downwards

• Opens upwards

What is the vertex of the parabola x = 3(y - 4)^2 - 93?

• (-93, 4)

• (93, -4)

• (4, -93)

• (-4, 93)

What is the axis of symmetry for a parabola with the equation x = 3(y - 4)^2 - 93?

• None

• Horizontal

• Diagonal

• Vertical