Identifying Parts of Quadratics

Review of Standard and Vertex Forms of Quadratics & Introducing

Factored Form of a Quadratic

By the end of this lesson, you will be able to identify all parts of a quadratic function graph:

• ​Axis of Symmetry

• Maximum / Minimum

• Vertex

• x-intercepts

• y-intercepts

• Factored Form of a Quadratic

Multiple Choice

1) What type of equation is graphed ?

• linear

• quadratic

• exponential

• constant

Definition:

A quadratic equation forms a parabola, a "U" shaped graph.

In standard form, a quadatric is in the form y = ax² + bx + c

In vertex form, a quadratic is in the form y = a(x - h)² + k

In factored form, a quadratic is in in the form y = a(x - r₁)(x - r₂)

Fill in the Blank

At what x value is the graph symmetrical? Type in a number based off the graph. x = ?

Axis of symmetry

The imaginary vertical line through the vertex of the parabola.

The axis of symmetry divides the parabola into two symmetrical parts.

The axis of symmetry is written like this: x = h

*h is the x-coordinate of the vertex.

Multiple Choice

Does this quadratic show a maximum or minimum value?

• Maximum

• Minimum

Maximum

A quadratic has a maximum / "High" point when it is an upside down "U" as shown in the graph.

Fill in the Blank

What is the low point of this quadratic? Write your answer as a coordinate (x, y).

(

,

-

)

Minimum

A quadratic has a minimum / "low" point when it is a normal "U" as shown in the graph.

Vertex

The highest or lowest point on the parabola.

Multiple Select

What are the x - intercepts of the quadratic shown?

*HINT: name the coordinate points where the parabola hits the x-axis (horizontal axis)

• (-1, 0) and (3, 0)

• (0, 2) and (0, -2)

• (0, -1) and (0, 3)

• (2, 0) and (-2, 0)

x- intercepts

where the graph intersects the x - axis

x-intercepts are also known as "zeroes" because they will always have 0 in the y-coordinate position

x-intercepts are also known as "roots"

NEW INFO:

Factored Form of a Quadratic Equation:

y = a(x - r₁)(x - r₂)

where r₁ and r₂ are the x-intercepts / roots / zeroes
(*remember, all of these words mean the same thing*)

​Ex: 
y =(x − 5)(x + 2)   has x-intercepts at  x = 5 and x = -2
(*we switch the signs because... we never listen to x, right?)

So the x-intercepts at (5, 0) and (-2, 0)

Labelling

Please label the graph.

Drag labels to their correct position on the image

x-intercept

Axis of Symmetry

Vertex

x-intercept

Multiple Choice

What are the x-intercepts of

f(x) = (x + 3)(x + 8)  ?

• (3,0) and (8,0)

• (-3,0) and (-8, 0)

• (-3, 0) and (8,0)

• (3, 0) and (-8, 0)

Multiple Choice

What are the x-intercepts of

y = (x − 6)(x + 4)  ?

• (3, 0) and (-2, 0)

• (-6, 0) and (4, 0)

• 
  (6, 0) and (-4, 0)

• (-6, 0) and (-4, 0)

Multiple Choice

What are the x-intercepts of the parabola?

y = -3(x + 5)(x - 9)

• (-5, 0) and (9, 0)

• (5,0) and (-9, 0)

• (5, 0) and (9, 0)

• (-3, 0) and (5, 0)and (-9, 0)

Multiple Choice

State the direction of opening of the following: y = -(x+3)(x-2)

• left

• up

• down

• right

Multiple Choice

What are the x-intercepts of the quadratic?

• (2, 0) and (4, 0)

• (2, 0) and (5, 0)

• (-2, 0) and (-5, 0)

• 
  (-2, 0) and (-4, 0)

Multiple Choice

What is the green dot on the parabola called?

• Vertex

• Roots

• x-intercept

• Axis of Symmetry