Standard and Vertex Forms and Graphs of Quadratic Functions

In the vertex form of a quadratic function, ___ is the vertex and ___ is the axis of symmetry.

(a)  

Tags

CCSS.HSF-IF.C.7A

​ "a" determines the width and direction of the parabola in both the standard form and vertex form of a quadratic function.

If "a" is positive, then the parabola will open ​ (a)   like a ​ (b)   .

If "a" is negative, then the parabola will open ​ (c)   like a ​ (d)   .

If "a" is negative, then the parabola will be reflected across the ​ (e)   .

• up
• smile
• down
• frown
• left
• right
• x-axis
• y-axis
• z-axis

Why use vertex form?

Vertex form shows the ___ on a quadratic equation in respect to its ___ function, f(x) = x²

(a)  

For the function, f(x) = -(x + 5)² − 1,

identify the vertex and axis of symmetry.

• Vertex: (-5, -1)

  Axis of symmetry:

  x = -5

• Vertex: (-5, 1)

  Axis of symmetry:

  x = -5

• Vertex: (5, -1)

  Axis of symmetry:

  x = 5

• Vertex: (0, -1)

  Axis of symmetry:

  x = 0

• Vertex: (-1, -5)

  Axis of symmetry:

  x = -1

For the quadratic inequality y ≥ 4(x+1)² − 7,

give the vertex and axis of symmetry, then graph the inequality.

• 
• 
• 
• 
• 

Tags

CCSS.HSF-IF.C.7A

Match the following vocabulary

• Vertex Form of a Quadratic Equation

• Standard Form of a Quadratic Equation

• f(x) = a(x−h)²+k

• Vertex

• f(x) = ax²+bx+c

• Parabola

• The turning point of the parabola; either a minimum or a maximum

• Axis of Symmetry

• U-shaped curve created by a quadratic equation

If a parabola has a vertex at (-3, 2),
where is the axis of symmetry?

• y = -2
• x = 3
• x = -3
• y = 2

Determine if the function has a minimum or maximum.

Then find the axis of symmetry and the vertex and y-intercept.

f(x) = -x² + 6x

Minimum / Maximum? ​ (a)  

Axis of Symmetry: ​ (b)  

Vertex: ​ (c)  

y-intercept: ​ (d)  

• Maximum
• Minimum
• x = 3
• x = 0
• x = 6
• (3, 9)
• (-1, 6)
• (0, 0)
• (-6, 0)
• (0, 6)

State the domain and range of the function.

f(x) = 2x² − 8x + 6

Domain: ​ (a)  

​ Range: ​ (b)  

• {ℝ}
• {y| y ≥ -2}
• {x| x ≥ -2​}
• {y| y > -2​}
• {y| y < -2​}
• {y| y ≤ -2​}
• {x| x > -2​}
• {x| x < -2​}
• {x| x ≤ -2​}

Graph the function.

f(x) = -x² + 5

​

Tags

CCSS.HSF-IF.C.7A