F25 Alg 1B Lesson 10.3 Discriminant

​Lesson 10.3: The Discriminant

How many real number solutions can we expect?

Multiple Choice

1 What does the discriminant tell us?

• The maximum or minimum

• The y-intercept

• The number and type of solutions

• The axis of symmetry

Multiple Choice

The discriminant is

• ax² + bx + c

• √(b² - 4ac)

• b² - 4ac

• b² + 4ac

Multiple Choice

Which of the following best describes the role of the discriminant in a quadratic equation?

• It determines the number and type of solutions.

• It gives the vertex of the parabola.

• It finds the axis of symmetry.

• It calculates the maximum value.

Multiple Select

To prepare to do the quadratic formula,

set one side equal to zero:

-2x² = 7x - 4

• -2x² - 7x + 4 = 0

• -2x² +7x - 4 = 0

• -2x² - 7x - 4 = 0

• -2x² + 7x + 4 = 0

Multiple Choice

When in standard form, what is the value of a, b and c in this quadratic?

8x² + 3x - 6 = 3x

• a = 8 b = 0 c = -6

• a = 8 b = 6 c = -6

• a = 8 b = -6 c = 0

• a = 8 b = 3 c = -6

Multiple Choice

Determine the value of the discriminant and describe the number and type roots for the following:

x² + 7x + 13

• 101, 2 solutions

• 3, 2 solutions

• -101, no solution

• -3, no solution

Drag and Drop

When the discriminant is

Placeholder

there will be zero real number solutions.

Drag these tiles and drop them in the correct blank above

Negative

Zero

Positive

Multiple Choice

Solve for the discriminant of the given equation -2x² -6x=0

• -36

• 36

• 0

• 44

Multiple Choice

When in standard form, what is the value of a, b and c in this quadratic?

9x² + 4x - 6 = -5x + 8

• a = 14 b = 4 c = -14

• a = 9 b = 9 c = -14

• a = 9 b = -1 c = 2

• a = 9 b = -9 c = 14

Multiple Choice

What is the discriminant and how many solutions would this quadratic have?

-4x² - 8x - 8 = -4

• 0, No Solutions

• 0, 1 Solution

• 128, 2 Solutions

• 128, 1 Solution

Multiple Choice

For which values of the discriminant will a quadratic equation have two distinct real solutions? Select all that apply.

• Positive

• Zero

• Negative

• Complex

Match

Match the following.

• Graph of

Two x-intercepts

One x-intercept

No x - intercept

• Two x-intercepts

• One x-intercept

• No x - intercept

• $$y=ax^2+bx+c$$

Multiple Choice

How many solutions are there?

• 2 imaginary

• 1 repeated real

• 2 real

• 0

Multiple Choice

How many solutions are there?

• 0 real

• 1 repeated real

• 2 real

• 0

Multiple Choice

When looking at a quadratic graph, the solution(s) are always the _____________.

• y-intercept

• vertex

• x-intercept(s)

• axis of symmetry

Multiple Choice

3 For the function above, is the discriminant positive, negative, or zero?

• Positive

• Negative

• Zero

Labelling

Label the following

Drag labels to their correct position on the image

two imaginary solutions

two real solutions

no

one

two

one real solution

Dropdown

Solve the equation:

0 = $$11g^2-8g+7$$ .

The solutions are ​

Select answer

​ or

Select answer

Match

Match the following values of the discriminant to their number of solutions.

• x>0

• x=0

• x<0

2

1

0

• 2

• 1

• 0

Labelling

Fill in quadratic formula

Drag labels to their correct position on the image

b²-4ac

2a

b^2

-b^2-4ac

b^2+4ac

-2a

-b

a^2

4ac-b^2

b