Quadratic Formula & Discriminant

Quadratic Formula
&
Discriminant

The Discriminant will tell you the number of solutions you have.

Discriminant = b² - 4ac

If the discriminant is:

• positive , then you have 2 real solutions

• negative, then you have 2 imaginary solutions (no real)

• zero - then you have one solution (double root)

Quadratic Formula

Multiple Choice

Given the quadratic

$$f\left(x\right)=2x^2-8x+13$$  , what is the "b" value?

• b = 2

• b = -8

• b = 13

• b = 8

Multiple Choice

What is the value of (-3)^2?

• 9

• -9

• 6

• -6

Multiple Choice

What is the value of -(-7)?

• -7

• 7

• 8

• -8

Multiple Choice

What does the discriminant tell us about a quadratic function?

• The maximum or minimum value

• The y-intercept

• The number and type of solutions

• The axis of symmetry

Multiple Choice

What is the formula for the discriminant of a quadrartic equation?

• $$\frac{-b}{2a}$$  

• $$b^2-4ac$$  

• $$ax^2+bx+c$$  

• $$\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$  

Multiple Choice

If the discriminant is equal to -2, how many real solutions are there?

• None

• One

• Two

• Infinite

Multiple Choice

If the discriminant of the quadratic equation is equal to 4, how many real solutions are there?

• None

• One

• Two

• Infinite

Multiple Choice

If the discriminant of the quadratic equation is equal to 0, how many real solutions are there?

• None

• One

• Two

• Infinite

Multiple Choice

Which is the correct set-up of the discriminant for:
$$3x^2-19x+20=0$$  

• $$\left(-19\right)^2-4\left(3\right)\left(20\right)$$  

• $$\left(-19\right)^2-4\left(3\right)\left(-20\right)$$  

• $$\left(-20\right)^2-4\left(3\right)\left(-19\right)$$  

• $$-\left(-19\right)^2-4\left(3\right)\left(-20\right)$$  

Multiple Choice

What is the discriminant of this equation?

3x² + 8x = 0

• 64

• 52

• 9

• 0

Multiple Choice

For the function below, determine if the discriminant is positive, negative, or zero?

___________

y = x² + 4x + 4

• Positive

• Negative

• Zero

Multiple Choice

What is the value of the discriminant of 6x² − 2x − 3 = 0

• 76

• 29

• 68

• none of these

Multiple Choice

What is the value of the discriminant of -2x² − x − 1 = 0

• 76

• -7

• 9

• none of these

Multiple Choice

____________

For the function above, determine whether the discriminant is positive, negative, or zero.

• Positive

• Negative

• Zero

1) Determine the a, b, & c values

1) Determine the a, b, & c values





ANSWER:

a=3 b=5 c= -2

3) Simplify under the radical



ANSWER: 49

When you have a perfect square under the radical, you can find two answers that can be written as fractions. (Or whole numbers!)




*It means that it was possible to factor the original equation!

4) Solve the rest of the quadratic formula!

4) Solve the rest of the quadratic formula!

ANSWER: x= 2/3 and x= -2

PRACTICE....

Multiple Choice

What are the x-intercepts of

$$f\left(x\right)=4x^2-x-7$$  ?

• $$x=\frac{1\pm\sqrt{113}}{2}$$  

• $$x=\frac{1\pm\sqrt{111}}{8}$$  

• $$x=\frac{1\pm\sqrt{113}}{8}$$  

• $$x=\frac{4\pm\sqrt{111}}{2}$$  

Multiple Choice

What are the zeros of

$$f\left(x\right)=-2x^2+3x+1$$  ?

• $$x=\frac{3\pm\sqrt{17}}{4}$$  

• $$x=\frac{-3\pm\sqrt{18}}{4}$$  

• $$x=\frac{3\pm\sqrt{17}}{-4}$$  

• $$x=\frac{3\pm\sqrt{18}}{2}$$  

Multiple Choice

What are the zeros of

$$f\left(x\right)=x^2+7x-18$$  ?

• $$x=-2,\ -9$$  

• $$x=2,\ -9$$  

• $$x=-2,\ 9$$  

• $$x=2,\ 9$$