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Algebra II : Intermediate Single-Variable Algebra

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #18 : Discriminants

What is the discriminant? $y=-\frac{1}{2}x^2+2x+6$

Possible Answers:

Correct answer:

Explanation:

This equation is already in the form of y=ax^2+bx+c .

$a=-\frac{1}{2}$

b=2

c=6

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

b^2-4ac

Substitute the terms into the expression and solve.

$(2)^2-4(-\frac{1}{2})(6) = 4+12 = 16$

The answer is:

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Example Question #19 : Discriminants

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

Possible Answers:

Correct answer:

Explanation:

Identify the coefficients for the polynomial y=ax^2+bx+c .

a=-3

b=0

c=2

Write the expression for the discriminant. This is the expression inside the square root from the quadratic formula.

D=b^2-4ac

Substitute the numbers.

D=(0)^2-4(-3)(2) = 24

The answer is:

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Example Question #11 : Discriminants

Evaluate the discriminant given the parabola: y=x^2-x-1

Possible Answers:

Correct answer:

Explanation:

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

b^2-4ac

Identify the values of each variable. This corresponds to the coefficients of the quadratic in standard form:

y=ax^2+bx+c

a=1, b=-1,c=-1

Substitute these values into the expression to determine the discriminant.

b^2-4ac = (-1)^2-4(1)(-1) = 1+4 = 5

The discriminant is:

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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 #271 : Intermediate Single Variable Algebra

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 #272 : Intermediate Single Variable Algebra

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

Possible Answers:

1521

943

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 #273 : Intermediate Single Variable Algebra

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

Possible Answers:

601

421

121

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 #274 : Intermediate Single Variable Algebra

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

Possible Answers:

225

175

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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Algebra II : Intermediate Single-Variable Algebra

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #18 : Discriminants

Example Question #19 : Discriminants

Example Question #11 : Discriminants

Example Question #1411 : Algebra Ii

Example Question #1412 : Algebra Ii

Example Question #1411 : Algebra Ii

Example Question #271 : Intermediate Single Variable Algebra

Example Question #272 : Intermediate Single Variable Algebra

Example Question #273 : Intermediate Single Variable Algebra

Example Question #274 : Intermediate Single Variable Algebra

All Algebra II Resources

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