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Algebra II : Quadratic Equations and Inequalities

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #1411 : Algebra Ii

Determine the discriminant for the function: y=3x^2-2x-3

Possible Answers:

Correct answer:

Explanation:

Write the formula for the discriminant. This is the inner quantity of the square root of the quadratic formula.

b^2-4ac

The polynomial is already written in the form of: y=ax^2+bx+c

Identify the coefficients for y=3x^2-2x-3 .

a=3, b=-2, c=-3

Substitute these values to find the discriminant.

b^2-4ac = (-2)^2-4(3)(-3) = 4+36 = 40

The discriminant is:

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Example Question #1412 : Algebra Ii

Determine the discriminant of: y=3x^2-9x-1

Possible Answers:

Correct answer:

Explanation:

The discriminant is the inner quantity of the radical of the quadratic formula.

Write the expression for the discriminant.

b^2-4ac

The polynomial is already in y=ax^2+bx+c format. Identify the coefficients of the polynomial.

a=3, b=-9, c=-1

Substitute these values to find the discriminant.

b^2-4ac = (-9)^2-4(3)(-1) = 81+12 = 93

The discriminant is:

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Example Question #1411 : Algebra Ii

Determine the discriminant of the following equation: y=8x^2-6x

Possible Answers:

192

Correct answer:

Explanation:

Write the formula for the discriminant. This is the term inside the square root of the quadratic equation.

D=b^2-4ac

The polynomial is written in the form: y=ax^2+bx+c

a=8, b=-6, c=0

Substitute the values into the discriminant formula.

D=b^2-4ac = (-6)^2-4(8)(0) = 36

The answer is:

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Example Question #21 : Discriminants

Find the discriminant for the quadratic equation y=2x^2 + 5x -12

Possible Answers:

121

Correct answer:

121

Explanation:

The discriminant is found by using the formula b^2 -4ac . In this case:

5^2 - 4(2)(-12 ) = 25 + 96 = 121

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Example Question #22 : Discriminants

Find the discriminant for the quadratic equation y=4x^2 +17x -77

Possible Answers:

943

1521

Correct answer:

1521

Explanation:

The discriminant is found using the formula b^2 - 4ac . In this case:

17^2 - 4(4)(-77 ) = 289 + 1,232 = 1,521

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Example Question #23 : Discriminants

Find the discriminant for the quadratic equation y=6x^2 -19 x + 10

Possible Answers:

421

121

601

Correct answer:

121

Explanation:

To find the discriminant, use the formula b^2 - 4ac . In this case:

(-19)^2 - 4(6)(10) = 361 - 240 = 121

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Example Question #24 : Discriminants

Find the discriminant for the quadratic equation y=2x^2 -5x - 25

Possible Answers:

175

225

Correct answer:

225

Explanation:

To find the discriminant, use the formula b^2 - 4ac . In this case:

(-5)^2 - 4(2)(-25) = 25 + 200 = 225

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Example Question #21 : Discriminants

Determine the discriminant of the quadratic: y=4x^2-3

Possible Answers:

$\textup{There is no discriminant.}$

Correct answer:

Explanation:

The quadratic function is in the form of y=ax^2+bx+c .

The discriminant is the term inside the square root of the quadratic function defined as: D=b^2-4ac

Identify the coefficients.

a=4,b=0, c=-3

Substitute the values into the equation.

D=0-4(4)(-3) = 48

The answer is:

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Example Question #1418 : Algebra Ii

Determine the discriminant of the following polynomial: y=3-6x^2-5x

Possible Answers:

Correct answer:

Explanation:

Reorder the equation in y=ax^2+bx+c standard format.

y=3-6x^2-5x

y=-6x^2-5x+3

The discriminant is the term inside the square root of the quadratic equation.

D= b^2-4ac

Identify and substitute the coefficients for each term of the polynomial in standard form.

D= (-5)^2-4(-6)(3) =25+72 = 97

The answer is:

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Example Question #1421 : Algebra Ii

Determine the discriminant: y=6-x^2

Possible Answers:

Correct answer:

Explanation:

Rewrite the equation in standard form.

y=ax^2+bx+c

$y=6-x^2 \rightarrow y=-x^2+0x+6$

In this format, we can identify the coefficients of a, b, and c.

a=-1, b=0, c=6

The discriminant is the term inside the square root of the quadratic equation.

D=b^2-4ac

Substitute the known values and solve.

D=0^2-4(-1)(6) = 24

The answer is:

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Algebra II : Quadratic Equations and Inequalities

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #1411 : Algebra Ii

Example Question #1412 : Algebra Ii

Example Question #1411 : Algebra Ii

Example Question #21 : Discriminants

Example Question #22 : Discriminants

Example Question #23 : Discriminants

Example Question #24 : Discriminants

Example Question #21 : Discriminants

Example Question #1418 : Algebra Ii

Example Question #1421 : Algebra Ii

All Algebra II Resources

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