Key Features from Equations

​Key Features from Equations

By JANICE COLEMAN

Three Forms You Should Know:

• Standard Form

• Vertex Form

• Factored Form

Standard Form: Minimum

f(x) = Ax² + Bx + C

If A is positive, the graph opens up
It has a minimum

Standard Form: Maximum

f(x) = -Ax² + Bx + C

If A is negative, the graph opens down
It has a maximum

Standard Form: y-intercept

C is always the y-intercept

​f(x) = -Ax2 + Bx + C

​f(x) = Ax2 + Bx + C

Multiple Choice

Which of the following could be a graph of f(x) = 2x² + 3x + 1?

Multiple Choice

Which of the following could be a graph of f(x) = -2x² + 3x - 1?

Multiple Choice

Which of the following could be a graph of f(x) = -2x² + 3x + 1?

Multiple Choice

Which of the following could be a graph of f(x) = 2x² + 3x - 1?

Vertex Form: vertex

f(x) = (x-h)² + k

Change the sign of the number inside the parentheses (crazy x rule) - it is the x of your vertex


The number outside the parentheses is the y of your vertex.

Vertex Form: vertex

f(x) = (x-3)² + 6

The vertex is (3 , 6)

Vertex Form: vertex

f(x) = (x+3)² + 6

The vertex is (-3 , 6)

Multiple Choice

What is the vertex of the following equation?

f(x) = (x - 4)² + 7

• (4, 7)

• (7, 4)

• (-4, 7)

• (-4, -7)

Multiple Choice

What is the vertex of the following equation?

f(x) = (x + 4)² + 7

• (4, 7)

• (7, 4)

• (-4, 7)

• (-4, -7)

Multiple Choice

What is the vertex of the following equation?

f(x) = (x + 4)² - 7

• (4, 7)

• (7, 4)

• (-4, 7)

• (-4, -7)

Multiple Choice

What is the vertex of the following equation?

f(x) = (x - 4)² - 7

• (4, -7)

• (7, 4)

• (-4, 7)

• (-4, -7)

Vertex Form: minimum/maximum

f(x) = (x+h)² + k

The sign in front of the parentheses determines whether the graph opens up or down.
The minimum or maximum is the y of the vertex

Vertex Form: minimum/maximum

f(x) = (x+3)² + 2

The sign in front of the parentheses is positive so it opens up - it has a minimum at 2.

Vertex Form: minimum/maximum

f(x) = -(x+3)² + 2

The sign in front of the parentheses is positive so it opens down - it has a maximum at 2 .

Multiple Choice

Which statement is true about the following equation?

f(x) = (x + 3)² + 1

• It has a minimum at 1

• It has a maximum at 1

• It has a minimum at -3.

• It has a maximum at -3

Multiple Choice

Which statement is true about the following equation?

f(x) =-2 (x + 3)² + 1

• It has a minimum at 1

• It has a maximum at 1

• It has a minimum at -3.

• It has a maximum at -3

Factored Form: x-intercept

f(x) = (x-r)(x-s)

r is one of the x-intercepts
s is the other x-intercept

Factored Form: x-intercept

f(x) = (x-r)(x-s)

r is one of the x-intercepts
s is the other x-intercept

Factored Form: x-intercept

f(x) = (x-6)(x+2)

the roots are (6, 0) and (-2, 0)

Because of the -, the crazy x rule applies.

Multiple Select

What are the roots of the following equation?

f(x) = (x + 2)(x-5)

• -2

• -5

• 2

• 5

Multiple Select

What are the roots of the following equation?

f(x) = (x - 2)(x+5)

• -2

• -5

• 2

• 5

Choose the form that tells you the answer

y-intercept - standard form
min or max - standard form
y-intercept - standard
what is the minimum - vertex form
what is the maximum - vertex form
what are the roots - factored form.

Multiple Choice

Which form would you use to find the following?

Does it have a minimum or maximum?

• standard form

• vertex form

• factored form

Multiple Choice

Which form would you use to find the following?

Does it have a minimum or maximum?

• standard form

• vertex form

• factored form

Multiple Choice

Which form would you use to find the following?

What is the value of the minimum or maximum?

• standard form

• vertex form

• factored form

Multiple Choice

Which form would you use to find the following?

What is the y-intercept?

• standard form

• vertex form

• factored form

Multiple Choice

Which form would you use to find the following?

What is the x -intercept?

• standard form

• vertex form

• factored form

Multiple Choice

Which form would you use to find the following?

What is the highest point the rocket reached?

• standard form

• vertex form

• factored form

Multiple Choice

Which form would you use to find the following?

How long did it take the rocket to hit the ground?

• standard form

• vertex form

• factored form

Multiple Choice

Which form would you use to find the following?

How high off the ground was the rocket when it was launched?

• standard form

• vertex form

• factored form