Vertex to Standard Form NOTES

Vertex Form of a Quadratic Review

y = a(x - h)² + k

(h, k) is the vertex

a tells you if the parabola is concave up or down and determines the shape of parabola

Axis of Symmetry: x = h (x = the x-coordinate of the vertex)

Drag and Drop

In Vertex Form, the Axis of Symmetry equation is ​

Placeholder

Drag these tiles and drop them in the correct blank above

x = h

(0,0)

Multiple Choice

In Vertex Form, the vertex is represented by:

• (k, h)

• (h, k)

• (0, 0)

• (1, 2)

Draw

What shape is the graph of a quadratic? What is it called?

Multiple Select

When does a quadratic graph have a MAXIMUM vertex?

• when it is concave down

• when it is concave up

• when a is negative

• when a is positive

Multiple Select

When does a quadratic graph have a MINIMUM vertex? (select all that apply)

• when the graph is concave down

• when the graph is pretty

• when a is positive

• when the graph is concave up

Draw

Sketch a picture of a quadratic graph and label the vertex and axis of symmetry

Drag and Drop

The axis of symmetry is a ​

Placeholder

and the vertex is a ​

Placeholder

Drag these tiles and drop them in the correct blank above

straight line

coordinate point

minimum

maximum

parabola

Standard Form of a Quadratic Review

y = ax² + bx + c

example:
y = 2x² - 12x + 17

​a is 2
b is -12
c is 17

Multiple Select

What is the equation of a quadratic in Standard Form? (select all that apply)

• $$y\ =a\left(x-h\right)^2+k$$

• $$f\left(x\right)=\ a\left(x-h\right)^2+k$$

• $$y=ax^2+bx+c$$

• $$f\left(x\right)=ax^2+bx+c$$

​

Standard Form of a Quadratic

y = ax² + bx + c

example:
y = 2x² - 12x + 17

​a is 2
b is -12
c is 17

​How to find the Axis of Symmetry

​Step 1: Plug in a and b into the equation
Step 2: Simplify (use a calculator)

​

Standard Form of a Quadratic

y = ax² + bx + c

example:
y = 2x² - 12x + 17

​a is 2
b is -12
c is 17

​How to find the Axis of Symmetry

​Step 1: Plug in a and b into the equation




Step 2: Simplify (use a calculator)

Multiple Choice

What is the formula we use to find the Axis of Symmetry when a quadratic is in Standard Form?

• $$y\ =\ \frac{b}{2a}$$

• $$x=\frac{-b}{2a}$$

• $$y\ =\ x$$

• $$y\ =\ ax^2+bx+c$$

Fill in the Blanks

What is the axis of symmetry for the graph: $y\ =x^2+8x+20$

Fill in the Blanks

What is the axis of symmetry for the graph: $y=-3x^2-12x-15$

Standard Form of a Quadratic

Step 1: Find the axis of symmetry


Step 2: plug that number into the original equation to find the y-coordinate of the vertex


Step 3: the coordinate of the vertex is (axis of symmetry, number from step 1)

​a is 2
b is -12
c is 17

​How to find the VERTEX

​Step 1: Find the axis of symmetry:




Step 2: Plug this number into the original equation:





Step 3: These 2 numbers are the x & y coordinates of the vertex

​example:
y = 2x² - 12x + 17

​=

​Vertex is (3, -1)

Multiple Choice

How do you use the Axis of Symmetry to help you find the vertex of a quadratic function?

• plug the Axis of Symmetry number into the original equation to find the y-coordinate of the vertex

• plug that number into the coordinate grid

  (if this is your answer, go back and look at the previous slide)

• i have no idea

  (if this is your answer, go back and look at the previous slide)

• NO SOLUTION

  (if this is your answer, go back and look at the previous slide)

Fill in the Blanks

What is the vertex of the graph: $y=-x^2+4x-6$

HOW TO: Transform Vertex to Standard Form

Math Response

Write the equation in Standard Form:

-3(x+2)² -3

Type answer here

Correct Answer: -3x^2-12x-15

Deg^°

Rad

Math Response

Write the equation in Standard Form:

-(x-3)²-4

Type answer here

Correct Answer: -x^2+6x-13

Deg^°

Rad

Math Response

Write the equation in Standard Form:

2(x-5)² +2

Type answer here

Correct Answer: 2x^2-20x+52

Deg^°

Rad