Vertex to Standard Form NOTES

Presentation

•

Mathematics

•

12th Grade

•

Practice Problem

•

Hard

Jessica Orozco

FREE Resource

6 Slides • 16 Questions

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

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

and the vertex is a

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: $y\ =x^2+8x+20$

Type answer...

Fill in the Blanks

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

Type answer...

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: $y=-x^2+4x-6$

Type answer...

HOW TO: Transform Vertex to Standard Form

Math Response

Write the equation in Standard Form:

-3(x+2)²-3

Type answer here

Deg^°

Rad

Math Response

Write the equation in Standard Form:

-(x-3)²-4

Type answer here

Deg^°

Rad

Math Response

Write the equation in Standard Form:

2(x-5)² +2

Type answer here

Deg^°

Rad

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)

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