Discovering the Discriminant

​Another way to solve a quadratic...

Algebra 2

Multiple Select

Select ALL of the names for the points where the graph of a parabola crosses the x-axis.

• x-intercepts

• Zeroes

• Roots

• Solutions

Categorize

Options (9)

$$y=2x^2-3x-10$$  

$$y=3x^2+6x-4$$  

$$y=x^2+6x+8$$  

$$y=x^2-4x+4$$  

$$y=x^2-6x+9$$  

$$y=x^2$$  

$$y=-x^2+6x-11$$  

$$y=x^2-8x+20$$  

$$y=3x^2-x+2$$  

Graph each equation using Desmos. Classify the equations by the number of x-intercepts it has.

2 x-intercepts

1 x-intercept

0 x-intercepts

​Another way to solve a quadratic...

On your paper, Calculate the Discriminant for each Quadratic Equation.

Categorize

Options (9)

$$y=2x^2-3x-10$$  

$$y=3x^2+6x-4$$  

$$y=x^2+6x+8$$  

$$y=x^2-4x+4$$  

$$y=x^2-6x+9$$  

$$y=x^2$$  

$$y=-x^2+6x-11$$  

$$y=x^2-8x+20$$  

$$y=3x^2-x+2$$  

Using the discriminants that you calculated. Classify the equations by the value of the discriminant.

Positive

Zero

Negative

Match

What do you notice about the graphs and the discriminant?

• When the graph has 2 x intercepts.....

• When the graph has 1 x-intercept....

• When the graph has no x-intercepts...

the discriminant is positive.

the discriminant is zero.

the discriminant is negative.

• the discriminant is positive.

• the discriminant is zero.

• the discriminant is negative.