Comparison of Quadratic Functions Cellphone Problems

A quadratic function is shown below.

f(x) = x² – 10x + 16

Which of the following best represents the function in the form f(x) = a(x – h)² + k; what is the vertex of the parabola; and is the vertex a minimum or maximum?

• f(x) = (x – 5)² – 9; Vertex: (5, 9); Maximum

• f(x) = (x – 5)² – 9; Vertex: (–5, –9); Minimum

• f(x) = (x – 5)² – 9; Vertex: (5, –9); Minimum

• f(x) = (x – 2)(x – 8); Vertex: (2, 8); Maximum

A quadratic function is shown below.

f(x) = – x² – 4x – 2

Which of the following best represents the function in the form f(x) = a(x – h)2 + k; what is the vertex of the parabola; and is the vertex a minimum or maximum?

• f(x) = – (x + 4)² + 6; Vertex: (–4, 6); Maximum

• f(x) = (x + 4)² + 6; Vertex: (–4, 6); Minimum

• f(x) = – (x + 4)² + 6; Vertex: (4, 6); Maximum

• f(x) = – (x + 4)² - 10; Vertex: (–4, –10); Minimum

A quadratic inequality is shown below.

y ≤ –0.5(x – 3)² + 8

Which graph represents the solution to the quadratic inequality?

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• 
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The solution set for a quadratic inequality is shown on the coordinate grid.

Which inequality best represents the graph?

• y ≥ –x² + 6x – 5

• y > –x² + 6x – 5

• y ≥ –(x – 3)² + 2

• y > –(x – 3)² + 2

• –9 + 7i

• 3 + 47i

• 3 + 7i

Gladys threw a ball upward from a height of 1.5 meters. She collected the data using a motion detector comparing the height of a ball in meters as a function of time in seconds. Her collected data is shown in the table below.

Which function can best be used to relate the height of the ball, h(t), in terms of time, t?

• h(t) = –4.89t² + 9.95t + 1.52

• h(t) = 5.00 – 1.95ln(t)

• h(t) = 3.19(1.10)^t

Tamara launches a model rocket that sends tracking data to an app on her phone. After the rocket launches, the app collects the horizontal distance in feet the rocket has traveled from her phone, x, and the vertical distance in feet the rocket has traveled from her phone, y. The table shows some of the collected data from the rocket launch.

Which equation best models the collected data?

• y = –0.32x² + 30.72x + 5

• y = 9.93x + 180.31

• y = 49.53(1.06)^x

• y = –0.31x² + 30.31x + 3.96

A Civil War cannon is placed at the base of a hill. The cannon is fired at an angle toward the hill. The path of the cannon ball is parabolic and can be represented by y = –0.04x² + 4x + 1, where y represents the height of the ball in meters and x represents the horizontal distance of the ball from the cannon. The incline of the hill can be represented by the equation y = 0.8125x. How far will the cannon ball have moved horizontally from the cannon when it hits the hill?

• 60

• 70

• 80

• 90

Tommy was trying to solve the system of a linear equation and a quadratic equation shown below.

2x – y = –1

x² – 5x – y = –7

Tommy had completed the following steps in his algebraic solution process but could not factor the resulting quadratic, x² – 7x – 1, to complete the problem.

Step I: y = 2x + 1

Step II: x² – 5x – (2x + 1) = –7

Step III: x² – 5x – 2x – 1 = –7

Step IV: x² – 7x – 1 = –7

Determine the step in which Tommy made his mistake and justify your reasoning.

• Step I; Tommy should have transformed the first equation to y = 2x – 1.

• Step II; Tommy should have substituted the expression 2x + 1 in for each variable.

• Step III; Tommy should have distributed into the parentheses yielding the equation x² – 5x – 2x + 1 = –7.

• Step IV; Tommy must set the quadratic expression equal to 0 before factoring.

A system of a linear and a quadratic equation is shown below.

x + y + 12 = x²

x = y – 3

When solving the system algebraically, what is the solution?

• (–3, 0)

• (5, 8)

• (–3, 0) and (5, 8)

• (3, 6) and (–5,–2)