Standard Form of Quadratic Functions

What are coordinates of the vertex of a parabola often represented by?

• (x, y)

• (x₂, y₂)

• (h, k)

• (r₂, d₂)

A parabola has a vertex at (1,6) . Write in standard form.

• f(x) = x ²+ 5

• f(x) = x² - x + 7

• f(x) = x² -2x + 1

• f(x) = x² -2x + 5

What information do you need to write an equation in vertex form? Select all that apply.

• an ordered pair anywhere on the parabola

• the coordinates for the vertex

• the formula for standard form

• the formula for vertex form

Convert the equation from vertex form to standard form:

y = (x + 5)² - 4

• y = x² + 10x + 25

• y = x² + 10x - 29

• y = x² +5x + 21

• y = x² + 10x + 21

Your teacher gives you an equation in vertex form. If the "a" value is 1, select the statements below that are true.

• "a" will be1 in standard form

• "a" represents a vertical compression

• "a" will become 9 in standard form

• the parabola will open upward

• "a" describes the horizontal shift

Convert the equation into standard form:

y = -5(x + 2)² - 10

• y = -5x² - 20x - 30

• y = -5x² - 4x - 10

• y = 25x² + 100x + 90

• y = 25x² - 10x - 30

Which answer choice(s) below correctly show(s) an equation in vertex form and in its standard form? (There may be more than 1.)

• y = (x + 2)² + 3

  y =x² - 12x - 15

• y =(x + 5)² + 1

  y = x² + 10x + 26

• y = (x - 3)² - 6

  y =x² - 6x + 3

Write a quadratic in standard form with x - intercepts -8 and 5.

• y = x² +3x - 40

• y = x² - 13x - 40

• y = x² - 3x - 40

• y = x² + 3x + 40

Write a quadratic equation that passes through the points (-3, 0), (4, 0), and (2, 20).

• y = 2x² -x + 20

• y = x² - x - 12

• y = -2x² + 2x + 24

• y = -2x² - x - 12

Write a quadratic equation that passes through the points (-3, 0), (7, 0), and (6, -36)

• y = 6x² - 4x - 36

• y = 4x² - 16x - 84

• y = x² - 4x - 21

• y = 4x² - 4x - 21