Quadratic Roots

Quadratic Roots

By Patrick Resch

​What is a Quadratic Root?

​The point/s at which the parabola intersects the x-axis.

​​

You can also call these...​

1. ​Zeros

2. Solutions

3. x-intercepts​

​

Be prepared to write this on the next page ​

Multiple Select

What else can you call a quadratic root?

• Solution

• Zeros

• Y-Intercept

• X-Intercepts

​2 Solutions

​1 Solutions

​0 Solutions

​Graph the Following

x​	y​
-5	0​
-4​	-5​
-3​	-8​
-2​	-9​
-1​	-8​
0​	-5​
​1	0​

Multiple Select

What are the solution/solutions

• -5

• 5

• 1

• No Solution

Graph the Following

​x	​y
​-2	​9
-1​	4​
0​	1​
1​	0​
2​	1​
3​	4​
4​	9​

Multiple Choice

What are the solution/solutions

• -5

• 1

• 4

• No Solution

Graph the Following

X	​Y
-2​	-11​
-1​	-6​
0​	-3​
1​	-2​
2​	-3​
3​	-6​
4​	-11​

Multiple Choice

What are the solution/solutions

• -5

• 5

• 1

• No Solution

​Th Discriminant

​This Formula is used to determine the number of solutions for a Parabola 

​Standard Form

​The Discriminant

• If d>0 There are 2 solutions

• If d=0 There is 1 Solution

• If d<0 There is NO Solution​

Multiple Choice

What is the Standard Form for a quadratic?

• $$y=ax^2+bx+c$$  

• $$d=b^2-4ac$$  

• $$y=a\left(x-h\right)^2+k$$  

• $$y=mx+b$$  

Multiple Choice

What is the Vertex Form for a quadratic?

• $$y=ax^2+bx+c$$  

• $$d=b^2-4ac$$  

• $$y=a\left(x-h\right)^2+k$$  

• $$y=mx+b$$  

Multiple Choice

What is the Discriminant for a quadratic?

• $$y=ax^2+bx+c$$  

• $$d=b^2-4ac$$  

• $$y=a\left(x-h\right)^2+k$$  

• $$y=mx+b$$  

Multiple Choice

How many solutions for

$$y=x^2+5x+4$$  

• 1

• 2

• 0

Multiple Choice

How many solutions for

$$y=x^2+10x+25$$  

• 1

• 2

• 0

Multiple Choice

How many solutions for

$$y=4x^2-12x+9$$  

• 1

• 2

• 0

Multiple Choice

How many solutions for

$$y=-3x^2+5x-8$$  

• 1

• 2

• 0