Parts of the Parabola ALG 1

Parts of the Parabola

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• Always makes a U shape called parabola

• Note the vertex is the turning point of the graph

• The axis of symmetry (AOS) always passes through the vertex.

• There is ONE y-intercept

• There can be up to TWO x-intercepts

Multiple Choice

The graph of a quadratic function is called a

• Parabola
• Vertex
• Axis of Symmetry 
• Vertex Form

Labelling

Drag each feature to the correctly label the parabola.

Drag labels to their correct position on the image

x-intercept(s)

axis of symmetry

y-intercept

vertex

Vertex is a minimum

Vertex is a maximum

Multiple Choice

Which best describes the vertex of a parabola?

• Any point on the parabola.

• A point on the x-axis.

• The highest or lowest point of a parabola

• A point on the y-axis.

Dropdown

Consider this quadratic equation:     y = - x² - 2x + 3  

The parabola will open ​

Select answer

and the vertex will be a ​

Select answer

Multiple Choice

Does this parabola have a maximum or minimum?

• Maximum

• Minimum

Multiple Choice

What is the vertex?

• (4,-4)
• (2,0)
• (0,2)
• (6,0)

Range

Range

Multiple Choice

What is the Range?

• y ≥ 6

• y ≤ 6

• -10 ≤ y ≤ 6

• -10 ≤ x ≤ 6

Multiple Choice

What is the range of the function?

• y≤3

• y≥3

• All real numbers

• -6≤y≤3

Multiple Choice

What is the range?

• y≥-3
• y≥-1
• All real numbers
• y≤-1

Multiple Choice

What is the range of the graph?

• All real numbers
• y<0

• y ≥ 0
• x ≥ 0

Axis of Symmetry

Finding the Equation of the Axis of Symmetry

Multiple Choice

The axis of symmetry line passes through which point?

• y-intercept

• any random point

• vertex

• symmetrical point for the vertex

Multiple Choice

What is the name given to the dotted line?

• A) y-intercept

• B) axis of symmetry

• C) vertex

• D) root

Multiple Choice

What is the equation for axis of symmetry?

• y=3

• x=3

• x=5

• x=1

Multiple Choice

$$x\ =\ -\frac{b}{2a}$$  

What is the axis of symmetry for the following equation? $$f\left(x\right)=4x^2+8x+9$$  

• x=-8

• x=1

• x=-1

• x=2

Interval of Increase/Decrease

Multiple Choice

Where is the function decreasing?

• (-∞, -1)
• (-1, ∞)
• (-∞, 3)
• (-∞, ∞)

Multiple Choice

What is the interval of increase and decrease for the function?

• Increase: $$\left(-2,\infty\right)$$
  Decrease: $$\left(-\infty,-2\right)$$

• Increase: $$\left(-\infty,-2\right)$$
  Decrease: $$\left(-2,\infty\right)$$

• Increase: $$\left(-\infty,4\right)$$
  Decrease: $$\left(-\infty,\infty\right)$$

• Increase:undefined
  Decrease: undefined

Multiple Choice

What is the interval of decrease of this graph?

• $$x\ge4$$  

• $$-\infty<x<\infty$$  

• $$x>3$$

• $$x<3$$

Multiple Choice

What is the interval of increase of this graph?

• $$-0.5<x<3$$

• $$x<3$$

• $$x<4$$

• $$1<x<5$$

The y-intercept

We can find the

y-intercept without a graph

Multiple Choice

Identify the y-intercept

• (-1,-9)

• (0,-8)

• (-4,0)

• (2,0)

Multiple Choice

Find the y-intercept algebraically 
$$f\left(x\right)=3x^2\ -10x\ +\ 12$$  

• (12, 0)

• (0, 12)

• (0, 3)

• (0, -10)

The x-intercept(s)

We can find the

x-intercept(s) without a graph

Multiple Select

Identify the x-intercept(s)

Select all that apply.

• (-1,-9)

• (0,-8)

• (-4,0)

• (2,0)

Multiple Choice

Find the zeros of the quadratic function graphically $$f\left(x\right)\ =\ x^2+9x+20$$  

• (4, 0) and (5, 0)

• (-4, 0) and (-5, 0)

• (0, 4) and (0, 5)

• (0, -4) and (0, -5)