Answers Common Core Math III ASquare Root Functions

Square Root Functions — Unit test Answers

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When graphed, which parabola opens downward?

y = –3x2

y = (x – 3)2

y = one-third x squared

y = x2 – 3

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During a pumpkin launching contest, two pumpkins are launched at the same time. The path of pumpkin A is modeled by the equation y = –0.01x2 + 0.32x + 4. The path of pumpkin B is modeled by the equation y = –0.01x2 + 0.18x + 5. If x represents the distance the pumpkin traveled in feet and y represents height of the pumpkin in feet, what does the intersection point of the equations represent?

the height at which the pumpkins reach their greatest horizontal distance from the launch site

the horizontal distance of the pumpkins from the launch site when they reach the ground

the starting height of the pumpkins when they are at the launch site

the horizontal distance of the pumpkins from the launch site when their heights are the same

Which system is equivalent to

StartLayout Enlarged left-brace 1st row 5 minus x = 9 x squared 2nd row y = 5 minus x EndLayout

StartLayout Enlarged left-brace 1st row y = 9 y squared minus 90 y + 225 2nd row x = y minus 5 EndLayout

StartLayout Enlarged left-brace 1st row 5 + x = 9 x squared 2nd row y = 5 + x EndLayout

StartLayout Enlarged left-brace 1st row y = 3 x 2nd row x + 3 x = 5 EndLayout

Which equation is y = 3(x – 2)2 – (x – 5)2 rewritten in vertex form?

y = 3 (x minus seven-halves) squared minus StartFraction 27 Over 4 EndFraction

y = 2 (x minus 1) squared minus 11

y = 2 (x minus one-half) squared minus StartFraction 53 Over 4 EndFraction

y = 2 (x minus one-half) squared minus StartFraction 27 Over 2 EndFraction

Which equation is the inverse of y = x2 – 36?

y = plus-or-minus StartRoot x EndRoot + 6

y = plus-or-minus StartRoot x + 36 EndRoot

y = plus-or-minus StartRoot x EndRoot + 36

y = plus-or-minus StartRoot x squared + 36 EndRoot

Which equation represents a graph with a vertex at (1, –6)?

y = 3x2 + 6x – 3

y = 3x2 – 6x – 3

y = 3x2 – 8x – 1

y = 3x2 – 3x – 6

Which equation is y = –6x2 + 3x + 2 rewritten in vertex form?

y = negative 6 (x minus 1) squared + 8

y = negative 6 (x + one-fourth) squared + thirteen-eighths

y = negative 6 (x minus one-fourth) squared + nineteen-eighths

y = negative 6 (x minus one-half) squared + seven-halves

During a baseball game, a player hits a ball while a bird is flying across the field. Let t be the time in seconds since the ball is hit and h be the height in feet. The height of the baseball over time is modeled by the equation h = –16t2 + 65t and the height of a bird over time is modeled by the equation h = 8t + 20. What do the intersection points of the equations represent?

the height of the bird and the ball when the ball and the bird are the same distance from the player

the height of the bird and the ball when the player hits the ball

the time when the height of the ball and the bird are the same

the time when the ball and the bird hit the ground

What is one solution of the following system?

(–6, 0)

(–2, 4)

(0, –6)

(4, –2)

Which equation is the inverse of y = 7x2 – 10?

y = StartFraction plus-or-minus StartRoot x + 10 EndRoot Over 7 EndFraction

y = plus-or-minus StartRoot StartFraction x + 10 Over 7 EndFraction EndRoot

x = plus-or-minus StartRoot StartFraction x Over 7 EndFraction + 10 EndRoot

y = StartFraction plus-or-minus StartRoot x EndRoot Over 7 EndFraction plus-or-minus StartFraction StartRoot 10 EndRoot Over 7 EndFraction

For which value of m does the graph of y = 18x2 + mx + 2 have exactly one x-intercept?

For what values of m does the graph of y = mx2 – 5x – 2 have no x-intercepts?

m greater-than negative StartFraction 25 Over 8 EndFraction

m less-than negative StartFraction 25 Over 8 EndFraction

m less-than StartFraction 25 Over 8 EndFraction

m greater-than StartFraction 25 Over 8 EndFraction

If the discriminant of a quadratic equation is 4, 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.

Using the quadratic formula to solve 11x2 – 4x = 1, what are the values of x?

StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction StartRoot 15 EndRoot Over 11 EndFraction

StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction 2 StartRoot 15 EndRoot Over 11 EndFraction

StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction StartRoot 7 EndRoot Over 11 EndFraction

StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction StartRoot 7 EndRoot i Over 11 EndFraction

If , which inequality can be used to find the domain of f(x)?

StartRoot 4 x EndRoot greater-than-or-equal-to 0

4 x + 9 greater-than-or-equal-to 0

4 x greater-than-or-equal-to 0

StartRoot 4 x + 9 EndRoot + 2 greater-than-or-equal-to 0

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Square Root Functions — Unit test Answers

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