Graphing Parabolas Quiz Review

​Graphing Parabolas

By Kristin Tryan

Standard Form

Standard Form: The Vertex

Then, take the x-value and substitute it back into the equation to find the y.

Standard Form: The Vertex

Find the y-coordinate:

x = -b / 2a

x = -(4) / 2(2)

x = -1

Find the x-coordinate:

a = 2

b = 4

c = -6

Vertex: (-1, -8)

Drag and Drop

Given the following equation, find the vertex:

$$y=2x^2-8x+3$$



Vertex: (​​

Placeholder

,​

Placeholder

)

Drag these tiles and drop them in the correct blank above

2

-5

-2

5

1

-1

0

3

-3

4

Drag and Drop

Given the following equation, find the vertex:

$$y=x^2+6x+10$$



Vertex: (​​​​

Placeholder

,​ ​

Placeholder

)

Drag these tiles and drop them in the correct blank above

-3

1

-2

-1

0

2

3

-4

4

Vertex Form

• a is always at the beginning, before any ( ) or x. If you don't see it, it's 1!

• h is always in ( ) with x. If you don't see it, it's 0!

• k is always at the end. If you don't see it, it's 0!

Vertex Form: The Vertex

Vertex: (h, k)

h is a liar! Take the OPPOSITE of the value you see in the equation.

k is trustworthy. You don't have to change the sign of k.

Vertex Form: The Vertex

a = 1, h = 1, k = 0

Vertex: (1, 0)

y = (x - 1)²

a = 2, h = -3, k = -6

Vertex: (-3, -6)

y = 2(x + 3)² - 6

(Don't forget to change the sign of h from what you see in your equation!)

Dropdown

Given the quadratic equation, determine the vertex:

$$y=2\left(x-4\right)^2+7$$



Vertex: (​

Select answer

,​

Select answer

)

Dropdown

Given the quadratic equation, determine the vertex:

$$y=-3\left(x+6\right)^2$$



Vertex: (​

Select answer

,​

Select answer

)

Plotting Points

Use the a-value to help you!

After you plot your vertex on the graph, the adjacent (directly beside) points are determined by the a-value.

Move over one square to the right, then go up or down a number of squares that's equal to the a-value. Then, do the same moving to the left.

(If a is positive, move up, and if a is negative, move down.)

Start at the vertex.
Go right 1 and down 2, then plot a point.
Then, go back to the vertex and go left 1 and down 2, then plot a point.

If a = -2:

Start at the vertex.
Go right 1 and up 1, then plot a point.
Then, go back to the vertex and go left 1 and up 1, then plot a point.

If a = 1:

Plotting Points (Examples)

Graphing

Graph a parabola with a vertex at

(3, -4) and an a-value of 2.

(Drag and drop your vertex into place, then drag the other point to make the next point adjacent to the vertex. It does not matter if the point is to the right or to the left.

Graphing

Graph a parabola with a vertex at

(3, -4) and an a-value of 2.

(Drag and drop your vertex into place, then drag the other point to make the next point adjacent to the vertex. It does not matter if the point is to the right or to the left.

Graphing

Graph a parabola with a vertex at

(2, -1) and an a-value of -3.

(Drag and drop your vertex into place, then drag the other point to make the next point adjacent to the vertex. It does not matter if the point is to the right or to the left.