8.4 Vertex and Axis of Symmetry

Multiple Select

Which of the following statements are true about the axis of symmetry in a quadratic function?

• The axis of symmetry always passes through the vertex.

• It divides the parabola into two equal halves.

• The formula for the axis of symmetry is x = -b/2a.

• The axis of symmetry is always vertical.

Open Ended

Explain how to find the vertex of a quadratic function given in standard form. What steps are involved and why are they important?

Multiple Choice

Why is the concept of the axis of symmetry important when studying quadratic functions?

• It helps determine the maximum or minimum value of the function.

• It is used to find the roots of the function.

• It shows how the function behaves at infinity.

• It is only relevant for linear equations.

Multiple Choice

What is the y-intercept of $$y=x^2+6x+8$$ ?

• (0,8)

• (8,0)

• (6,0)

• (0,6)

Multiple Choice

Now find the axis of symmetry of $$y=x^2+6x+8$$ . Use $$x=-\frac{b}{2a}$$  

• x = -3
• x = -5
• x = -2
• x = -4

Now find the vertex by plugging in -3 to the function.

Multiple Choice

What is the vertex of $$y=x^2+6x+8$$ ?

• (-3, -1)
• (-3, -19)

• (-3, 35)

• (-3, -2)

Change the equation into factored form... like y=(x+m)(x+n)

Multiple Choice

What is $$y=x^2+6x+8$$ in factor form?

• y=(x - 2)(x - 4)

• y=(x + 3)(x + 5)

• y=(x + 2)(x + 4)

• y=(x + 1)(x + 8)

On the table fill in the point for the y-intercept, the x-intercepts, and the vertex. Then pick one point for each side of the vertex.

Graph your points.

Multiple Choice

What value of x are the solutions to $$y=\left(x+2\right)\left(x+4\right)$$ ?

• -2, -4
• 2, 4

• -2, 4

• 2, -4

• Factor out -1 first.
  Then factor the remaining trinomial.

• Next figure the solutions for x.

• Then write down the y-intercept and the x-intercepts on the table.

• Next calculate the axis of symmetry and the vertex.

• Then figure out two more points.

• Finally graph your points.

Drag and Drop

What is the axis of symmetry of the graph​

Placeholder

Drag these tiles and drop them in the correct blank above

(-1,0)

(5,0)

x = 2

y = -3

(0,1.5)

Drag and Drop

The vertex of the parabola is

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. The Axis of Symmetry passes through the ​

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which is represented by ​

Placeholder

format

The Axis of symmetry is identified using the ​ $$h$$ of the vertex making the axis of symmetry for the graph ​

Placeholder

Drag these tiles and drop them in the correct blank above

(6,-6)

Vertex

x = 6

(3,5)

y-inetrcept

(y,x)

y

-6

(h,k)

Math Response

What is the axis of symmetry of the following quadratic?

(Remember it is an equation like x=9 or y=8)

Type answer here

Correct Answer: x=1

Deg^°

Rad

Dropdown

The axis of symmetry for the function graphed is

​

Select answer

=​

Select answer

Math Response

What is the axis of symmetry of the graph?

(Remember it is an equation like x=9 or y=8)

Type answer here

Correct Answer: x=-3

Deg^°

Rad

Drag and Drop

The quadratic equation has ​

Placeholder

​ solutions.

The ​ ​​

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point of the parabola is ​ ​

Placeholder

.

The minimum value of the function is ​

Placeholder

.

The equation of the line of symmetry is x = ​

Placeholder

​ .

Drag these tiles and drop them in the correct blank above

2

minimum

-6

(-3,-5)

-3

-5

(-3,-5)

0

-4

Open Ended

Do you have any questions or would you like to know more about how to graph quadratic functions and find their key features?