Answers ALG 1 part 2 SHS onlineSolving Quadratic Equations: Completing the Square

Introduction to the Quadratic Formula Answers

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Which shows the correct substitution of the values a, b, and c from the equation 1 = –2x + 3x2 + 1 into the quadratic formula?Quadratic formula:

x = StartFraction negative (negative 2) plus or minus StartRoot (negative 2) squared minus 4 (3)(0) EndRoot Over 2(3) EndFraction

x = StartFraction negative (negative 2) plus or minus StartRoot (negative 2) squared minus 4 (3)(2) EndRoot Over 2(3) EndFraction

x = StartFraction negative (negative 2) plus or minus StartRoot (negative 2) squared minus 4 (3)(1) EndRoot Over 2(3) EndFraction

x = StartFraction negative 3 plus or minus StartRoot 3 squared minus 4 (negative 2)(0) EndRoot Over 2(negative 2) EndFraction

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Which statement is true about the quadratic equation 8x2 − 5x + 3 = 0?

The constant term is 8.

The constant term is −5.

The leading coefficient is 8.

The leading coefficient is −5.

What is the value of the discriminant, b2 − 4ac, for the quadratic equation 0 = x2 − 4x + 5, and what does it mean about the number of real solutions the equation has?

The discriminant is −4, so the equation has 2 real solutions.

The discriminant is −4, so the equation has no real solutions.

The discriminant is 35, so the equation has 2 real solutions.

The discriminant is 35, so the equation has no real solutions.

What are the values of a, b, and c in the quadratic equation –2x2 + 4x – 3 = 0?

a = 2, b = 4, c = 3

a = 2, b = 4, c = –3

a = –2, b = 4, c = 3

a = –2, b = 4, c = – 3

A student is deriving the quadratic formula. Her first two steps are shown.Step 1: –c = ax2 + bxStep 2:

division property of equality

factoring the binomial

completing the square

subtraction property of equality

The first step for deriving the quadratic formula from the quadratic equation, 0 = ax2 + bx + c, is shown.Step 1: –c = ax2 + bx

subtraction property of equality

completing the square

factoring out the constant

zero property of multiplication

Some of the steps in the derivation of the quadratic formula are shown.Step 4: Step 5: Step 6: Step 7:

Negative values, like −4ac, do not have a square root.

The ± symbol prevents the square root from being evaluated.

The square root of terms separated by addition and subtraction cannot be calculated individually.

The entire term b2 − 4ac must be divided by 2a before its square root can be determined.

What are the values of a, b, and c in the quadratic equation 0 = x2 – 3x – 2?

a = , b = 3, c = 2

a = , b = –3, c = –2

a = , b = 3, c = –2

a = , b = –3, c = 2

A student is deriving the quadratic formula. Her first two steps are shown.Step 1: –c = ax2 + bxStep 2:

division property of equality

factoring the binomial

completing the square

subtraction property of equality

What is the value of the discriminant for the quadratic equation –3 = –x2 + 2x?Discriminant = b2 – 4ac

–8

What is the value of the discriminant for the quadratic equation 0 = x + 2 + x2?Discriminant = b2 – 4ac

–9

–7

What is the value of the discriminant for the quadratic equation 0 = 2x2 + x – 3?Discriminant = b2 – 4ac

–25

–23

Determine the discriminant for the quadratic equation -3=x2+4x+1. Based on the discriminant value, how many real number solutions does the equation have?Discriminant = b2-4ac

What is the value of the discriminant for the quadratic equation 0 = x + 2 + x2?Discriminant = b2 – 4ac

–9

–7

Determine the discriminant for the quadratic equation 0=-2x2+3. Based on the discriminant value, how many real number solutions does the equation have?Discriminant = b2-4ac

Which shows the correct substitution of the values a, b, and c from the equation 1 = –2x + 3x2 + 1 into the quadratic formula?Quadratic formula:

x = StartFraction negative (negative 2) plus or minus StartRoot (negative 2) squared minus 4 (3)(0) EndRoot Over 2(3) EndFraction

x = StartFraction negative (negative 2) plus or minus StartRoot (negative 2) squared minus 4 (3)(2) EndRoot Over 2(3) EndFraction

x = StartFraction negative (negative 2) plus or minus StartRoot (negative 2) squared minus 4 (3)(1) EndRoot Over 2(3) EndFraction

x = StartFraction negative 3 plus or minus StartRoot 3 squared minus 4 (negative 2)(0) EndRoot Over 2(negative 2) EndFraction

Which statement is true about the quadratic equation 8x2 − 5x + 3 = 0?

The constant term is 8.

The constant term is −5.

The leading coefficient is 8.

The leading coefficient is −5.

Determine the discriminant for the quadratic equation -3=x2+4x+1. Based on the discriminant value, how many real number solutions does the equation have?Discriminant = b2-4ac

Which is the graph of a quadratic equation that has a positive discriminant?

On a coordinate plane, a parabola opens up. It goes through (negative 1, 4), has a vertex at (1, 0), and goes through (3, 4).

On a coordinate plane, a parabola opens up. It goes through (negative 3, 4), has a vertex at (negative 1, 0), and goes through (1, 4).

On a coordinate plane, a parabola opens up. It goes through (negative 2, 5), has a vertex at (0, 1), and goes through (2, 5).

On a coordinate plane, a parabola opens up. It goes through (negative 2, 3), has a vertex at (0, negative 1), and goes through (2, 3).

Determine the discriminant for the quadratic equation 0=-2x2+3. Based on the discriminant value, how many real number solutions does the equation have?Discriminant = b2-4ac

Some of the steps in the derivation of the quadratic formula are shown.Step 3: –c + = aStep 4a: –c + = aStep 4b: + = a

factoring a polynomial

multiplication property of equality

converting to a common denominator

addition property of equality

Some of the steps in the derivation of the quadratic formula are shown.Step 4: Step 5: Step 6: Step 7:

Negative values, like −4ac, do not have a square root.

The ± symbol prevents the square root from being evaluated.

The square root of terms separated by addition and subtraction cannot be calculated individually.

The entire term b2 − 4ac must be divided by 2a before its square root can be determined.

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Introduction to the Quadratic Formula Answers

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