Algebra 1 Module 10 Practice

• x = -2, 8

• x = -8, 2

• x = 4, -4

• x = 1/4, -1/4

Answer explanation

To find the roots of the equation x^2 + 6x - 16 = 0, we can factor it as (x + 8)(x - 2) = 0. Setting each factor to zero gives the roots x = -8 and x = 2, making the correct choice x = -8, 2.

Match each example that describes what type of function it represents.

The length of a rectangular field is 3 feet more than its width. If the area of the field is 154 square feet, what are the dimensions?

The width is __________ feet.

The length is __________ feet.

Answer explanation

To find when the javelin hits the ground, set y=0 in the equation: 0 = -16x^2 + 40x + 5. Solving this quadratic gives x ≈ 2.68 seconds. Thus, it takes approximately 2.7 seconds for the javelin to hit the ground.

Answer explanation

To solve \(x^2 + 10x + 19 = -3\), first rewrite it as \(x^2 + 10x + 22 = 0\). Completing the square gives \((x + 5)^2 = 3\). Thus, the answer is \(5\) and \(3\). The correct choices are 5 and 3.

Answer explanation

To solve the equation by completing the square, rewrite it as (x+5)^2 = 6. This gives x+5 = ±√6, leading to x = -5 ± √6. Rounding the solutions, we find x ≈ -3.27 or -6.73, which are the correct answers.

Match each dilation to it's correct function as it relates to the parent function by drawing a line from the function to it's matching dilation type.

Answer explanation

Refer to the graph to see how the graph moves based on each type of change.

Answer explanation

To find the time it takes for the package to reach the ground, set h = 0. Using the formula h = -16t^2 + h_0, with h_0 = 50, we solve 0 = -16t^2 + 50. This gives t = 1.77 seconds.

• Reflected over the x-axis

• Translated 4 units right

• Translated 4 units left

• Translated 5 units up

• Translated 5 units down

Answer explanation

The function h(x)=2(x-4)^2+5 is derived from the parent function f(x)=x^2. It is translated 4 units right (due to (x-4)) and 5 units up (due to +5). There are no reflections or left translations.