Quadratics and their graphs

Quadratics and their Graphs

by Andrew Schmitt

​What is a Quadratic?

• ​A Quadratic is a problem where the variable has a power of exactly 2.

• ​There are:

  • Quadratic expressions

    • ​No equal sign

  • ​Quadratic equations

    • ​Equal sign

  • ​Quadratic functions

    • ​2-variable equation (y , x)

​Graphs of quadratic functions

• ​​Remember that a graph shows all possible solutions to an equation.

• Functions deal with 2-variable equations (x , y).

• ​We can graph these on the coordinate plane.

Multiple Choice

Find the vertex

• (2, -2)
• x = 2
• (-2, 2)
• (0, 4)

Multiple Choice

What is the domain of the function?

• x ≥ 3

• x ≤ 3

• All real numbers

• -1 ≤ x ≤ 5

Multiple Choice

Find the decreasing interval

• x>-2

• x<-2

• x>2

• x<2

Multiple Choice

Which of the statements about the graph is FALSE?

• The vertex is a maximum

• There are two x-ints at x = -3 and x = 3

• The y-intercept is (0, 18)

• The range is y ≥ 18

Multiple Choice

Which statement about the graph is FALSE?

• The vertex is also an x-intercept

• The y-intercept is (0, -2)

• The axis of symmetry is x = 2

• The range is y ≥ 0

Multiple Choice

Which function has an axis of symmetry of x = 0?

• None of the above

Multiple Choice

Which function has a maximum at (2, 0)?

Multiple Choice

Determine the domain and range of the function

• Domain: All real numbers, Range: All real numbers

• Domain: x ≥ -4, Range: All real numbers

• Domain: All real numbers, Range: y ≥ -4

• Domain: -1 ≤ x ≤ 5, Range: y ≥ -4

Multiple Choice

Which function has a range y ≥ -4?

• None of the above

Multiple Choice

What are the x-intercepts?

• 0 and 2

• -4 and 0

• 2 and 3

• 0 and 4

Multiple Choice

Does the quadratic have a max/min vertex, and does the parabola open up/down?

• max / opens down

• min / opens up

• max / opens up

• min / opens down

Multiple Choice

What is the green dashed line called?

• roots or x-intercepts
• parabola
• axis of symmetry
• line of dashes
• dashing through the snow...

Multiple Choice

What is the significance of the ordered pair (0, -2) to the graph?

• It is the vertex

• It is an x-intercept

• It is the y-intercept

• It is the axis of symmetry

Multiple Choice

What is the significance of the ordered pair (2, -4) to the graph?

• It is the vertex

• It is an x-intercept

• It is the y-intercept

• It is the axis of symmetry

Multiple Select

What are the zeros of the function? Choose all that apply.

• x = 0

• x = -3

• x = -6

• y = 18

Multiple Choice

Which statement about the graph is FALSE?

• The vertex is (-3, 18)

• The vertex is a maximum

• The y-intercept is y = 0

• The axis of symmetry is y = -3

Multiple Choice

What is the significance of the ordered pair (3, 0) to the graph?

• It is the maximum point

• It is the vertex

• It is the y-intercept

• It is an x-intercept

Multiple Choice

Which function has an axis of symmetry of x = 0?

• None of the above

Multiple Choice

Which function has an x-intercept and y-intercept at (0, 0)?