Writing Quadratic Equations in Vertex & Standard Form

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) 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.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSA.CED.A.1

When given 3 or more ordered pairs on a parabola, which of the following is a method you can use to find the equation in standard form?

• Make a table of values. Find the rate of change (slope) and y-intercept.

• On the calculator, use STAT-EDIT to enter the values into L₁ and L₂. Then go to STAT>CALC and choose "QuadReg" (option 5).

• 3 ordered pairs will not give you enough information to find the equation for the parabola.

Tags

CCSS.HSA.REI.D.11

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

Your teacher gives you an equation in vertex form and wants you to convert it to standard form. Which one of the following describes the steps in the correct order?

• 1- Distribute the "a" value.

  2- Square the expression in parentheses.

  3- Combine like terms.

• 1- Sketch the graph on the coordinate plane.

  2- Identify 2 ordered pairs.

  3- Use STAT-EDIT and STAT>CALC-Option 4 (LinReg)

• 1- Square the expression in parentheses.

  2- Combine Like Terms.

  3- Distribute the "a" value.

• 1- Square the expression in parentheses.

  2- Distribute the "a" value.

  3- Combine like terms.

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

A parabola has a vertex at (-1.5,12.5) and passes through (0,8). Solve for "a" and write the equation in vertex form.

Formula: f(x) = a(x - h)² + k

• y = -1.5(12.5 - 8)²

• y = 2(x + 0)² + 8

• y = -2(x + 1.5)² + 12.5

• y = 8(x + 1.5)² - 12.5

• None of the above

Tags

CCSS.HSA.SSE.A.1

CCSS.HSA.CED.A.2

CCSS.HSG.GPE.A.2

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

Your teacher gives you an equation in vertex form. If the "a" value is -3, select the statements below that are true.

• "a" will be -3 in standard form

• "a" represents a vertical compression

• "a" will become 9 in standard form

• the parabola will open downward

• "a" describes the horizontal shift

Tags

CCSS.HSA.SSE.A.1

CCSS.HSF.BF.B.3

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

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