Answers 26MATH_Recovery_Alg1B22Completing the Square (Continued)

The Quadratic Formula Answers

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Which equation could generate the curve in the graph below?

y = 3x2 – 2x + 1

y = 3x2 – 6x + 3

y = 3x2 – 7x + 1

y = 3x2 – 4x – 2

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If the discriminant of a quadratic equation is equal to , which statement describes the roots?

There are two complex roots.

There are two real roots.

There is one real root.

There is one complex root.

Which equation can be solved using the expression for x?

10x2 = 3x + 2

2 = 3x + 10x2

3x = 10x2 – 2

10x2 + 2 = –3x

Which equation has the solutions ?

3x2 – 5x + 7 = 0

3x2 – 5x – 1 = 0

3x2 – 10x + 6 = 0

3x2 – 10x – 1 = 0

If x = –3 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the equation?

The discriminant is negative.

The discriminant is –3.

The discriminant is 0.

The discriminant is positive.

The first two steps in the derivation of the quadratic formula by completing the square are shown below. Which answer choice shows the correct next step?Step 1: Step 2:

mc031-3.jpg

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Using the quadratic formula to solve 7x2 – x = 7, what are the values of x?

StartFraction 1 plus-or-minus StartRoot 195 EndRoot i Over 14 EndFraction

StartFraction 1 plus-or-minus StartRoot 197 EndRoot Over 14 EndFraction

StartFraction 1 plus-or-minus StartRoot 195 EndRoot Over 14 EndFraction

StartFraction 1 plus-or-minus StartRoot 197 EndRoot i Over 14 EndFraction

Which equation shows the quadratic formula used correctly to solve 5x2 + 3x – 4 = 0 for x?

x = StartFraction negative 3 plus-or-minus StartRoot (3) squared minus 4 (5) (negative 4) EndRoot Over 2 (5) EndFraction

x = StartFraction 3 plus-or-minus StartRoot (3) squared + 4 (5) (negative 4) EndRoot Over 2 (5) EndFraction

x = StartFraction 3 plus-or-minus StartRoot (3) squared minus 4 (5) (negative 4) EndRoot Over 2 (5) EndFraction

x = StartFraction negative 3 plus-or-minus StartRoot (3) squared + 4 (5) (negative 4) EndRoot Over 2 (5) EndFraction

Using the quadratic formula to solve 5x = 6x2 – 3, what are the values of x?

StartFraction 5 plus-or-minus 3 StartRoot 11 EndRoot Over 12 EndFraction

StartFraction 5 plus-or-minus StartRoot 97 EndRoot Over 12 EndFraction

StartFraction 5 plus-or-minus StartRoot 47 EndRoot Over 12 EndFraction

StartFraction negative 5 plus-or-minus StartRoot 97 EndRoot Over 12 EndFraction

The graph of an equation with a negative discriminant always has which characteristic?

no x-intercept

no y-intercept

no maximum

no minimum

If is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the equation?

The discriminant is 0.

The discriminant is 6.

The discriminant is positive.

The discriminant is negative.

Which equation has the solutions ?

x2 + 2x + 4 = 0

x2 – 2x + 4 = 0

x2 + 2x – 4 = 0

x2 – 2x – 4 = 0

When deriving the quadratic formula by completing the square, what expression can be added to both sides of the equation to create a perfect square trinomial?