A. The other zero is irrational.
If one zero is rational and the quadratic equation has two distinct zeros, then the other zero must be irrational. This is because if both zeros were rational, then the quadratic could be factored into linear factors with rational coefficients, and this would contradict the assumption that a, b, and c are rational numbers.
Consider the quadratic equation ax^2 + bx + c = 0, where a, b, and c are rational numbers and the quadratic has two distinct zeros. If one zero is rational, which of the following is true of the other zero.
A. The other zero is irrational.
B. The other zero could be rational or irrational.
C. The other zero is not a real number.
D. The other zero is rational.
5 answers
The function g(x) = x^2 + 3. The function f(x) = g(x+2).
The function f(x) is shifted horizontally
select a value
A. 2 units to the left of g(x).
B .2 units to the right of g(x).
C. The function is not shifted horizontally from g(x).
The function f(x) is shifted vertically
A. 2 units up from g(x).
B. 2 units down from g(x).
C. The function is not shifted vertically from g(x).
The function f(x) is shifted horizontally
select a value
A. 2 units to the left of g(x).
B .2 units to the right of g(x).
C. The function is not shifted horizontally from g(x).
The function f(x) is shifted vertically
A. 2 units up from g(x).
B. 2 units down from g(x).
C. The function is not shifted vertically from g(x).
The function g(x) = x^2 + 3 is in the form y = x^2 with a vertical shift of 3 units upwards.
When we look at the function f(x) = g(x+2), it means the function g(x) is being shifted 2 units to the left, because it becomes g(x-2). This is a horizontal shift.
Therefore, the function f(x) is shifted horizontally 2 units to the left of g(x), which corresponds to option A.
Since the vertical shift on g(x) is 3 units upwards and there are no additional vertical shifts applied to f(x), the function f(x) is not shifted vertically from g(x), which corresponds to option C.
Therefore, the correct answers are:
The function f(x) is shifted horizontally: A. 2 units to the left of g(x).
The function f(x) is shifted vertically: C. The function is not shifted vertically from g(x).
When we look at the function f(x) = g(x+2), it means the function g(x) is being shifted 2 units to the left, because it becomes g(x-2). This is a horizontal shift.
Therefore, the function f(x) is shifted horizontally 2 units to the left of g(x), which corresponds to option A.
Since the vertical shift on g(x) is 3 units upwards and there are no additional vertical shifts applied to f(x), the function f(x) is not shifted vertically from g(x), which corresponds to option C.
Therefore, the correct answers are:
The function f(x) is shifted horizontally: A. 2 units to the left of g(x).
The function f(x) is shifted vertically: C. The function is not shifted vertically from g(x).
The quadratic function h(t) = -16.1t^2 + 150 models a ball's height, in feet, over time, in seconds, after it is dropped from a 15 story building.
From what height, in feet, was the ball dropped? blank
After how many seconds, rounded to the nearest hundredth, did the ball hit the ground? blank
From what height, in feet, was the ball dropped? blank
After how many seconds, rounded to the nearest hundredth, did the ball hit the ground? blank
To determine from what height the ball was dropped, we need to find the initial height. This is the constant term in the quadratic function. In this case, the constant term is 150, so the ball was dropped from a height of 150 feet.
To find out after how many seconds the ball hit the ground, we need to set h(t) = 0 and solve for t.
-16.1t^2 + 150 = 0
-16.1t^2 = -150
t^2 = 150 / 16.1
t^2 ≈ 9.31677
t ≈ √9.31677
t ≈ 3.05
Rounded to the nearest hundredth, the ball hit the ground after approximately 3.05 seconds.
To find out after how many seconds the ball hit the ground, we need to set h(t) = 0 and solve for t.
-16.1t^2 + 150 = 0
-16.1t^2 = -150
t^2 = 150 / 16.1
t^2 ≈ 9.31677
t ≈ √9.31677
t ≈ 3.05
Rounded to the nearest hundredth, the ball hit the ground after approximately 3.05 seconds.
1 answer