Write equations in Vertex and Standard Form from the graph

A parabola has a vertex at (1,6) and passes through (3,-18). Write the equation in vertex form.

Formula: f(x) = a(x - h)² + k

• f(x) = 3(x - 1)² - 18

• f(x) = -6(x - 1)² + 6

• f(x) = 6(x - 3)² - 18

• f(x) = -3(x + 1)² - 6

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

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

Tags

CCSS.HSA.SSE.A.2

CCSS.HSF.IF.C.8

Convert the equation from vertex form (shown) to standard form:

y = -3(x + 5)² - 4

Formula: y = ax² + bx + c

• y = 9x² - 15x + 21

• y = -3x² - 75x - 4

• y = 9x² + 90x + 221

• y = -3x² - 30x - 79

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

y = 2(x - 7)² + 4

Given the equation above, which of the following statements is FALSE?

• The graph opens upward.

• The vertex is at (7, 4).

• The parabola crosses the x-axis twice.

• The standard form is y= 2x² - 28x + 102.

• The axis of symmetry is x = 7.

Tags

CCSS.HSF-IF.C.7A

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

A parabola has a vertex at (6, 5) and passes through (10, -11). Which equation represents this parabola in vertex form?

Formula: f(x) = a(x - h)² + k

• -11 = a(10 - 6)² + 5

• y = -(10 - h)² + k

• y = -(x - 6)² + 5

• y = (x - 6)² + 5

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 = -3(x + 2)² + 3

  y = -3x² - 12x - 15

• y = 2(x + 5)² + 1

  y = 2x² + 20x + 51

• y = 0.5(x - 3)² - 6

  y = 0.5x² - 3x - 1.5

Which of the following statements are TRUE?

Select all that apply.

• The "a" value is positive.

• The y-intercept is positive.

• It has two zeros.

• The axis of symmetry is x = 1.

• The vertex is at (0, 5).

Tags

CCSS.HSF-IF.C.7A

Which of the following equations matches standard form of a quadratic?

• ax + by = c
• y = a(x - h)² + k
• y = ax² + bx + c
• y = mx + b

Which of the following equations is in vertex form?

• f(x) = x² + 6x - 2
• f(x) = (x - 1)² + 2

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8