In math class, Julia and Ricardo are analyzing the function f(x)=−x^2+4x−14. Julia thinks there are no real zeros in this function, and Ricardo says there is one real zero. Who is right?
A. Julia is right because the function has no real zeros.
B. Ricardo is right because the discriminant of this function is zero.
C. Ricardo is right because the function has one real zero.
D. Julia is right because the function has two real zeros.
5 answers
B. Ricardo is right because the discriminant of this function is zero.
its A
Apologies for the confusion. You are correct.
A. Julia is right because the function has no real zeros.
The discriminant of the function is negative, indicating that there are no real zeros in this case. Thank you for pointing that out.
A. Julia is right because the function has no real zeros.
The discriminant of the function is negative, indicating that there are no real zeros in this case. Thank you for pointing that out.
Observe the graph for the function f(x)=−2x^2+17x+1. Which statements about this graph are true? Select all that apply
A. The graph has zeros near 0 and 8.5.
B. There are two real zeros in this graph.
C. There are no real zeros in this graph.
D. The graph has a zero near 35.
E. The graph has only one real zero.
F. There are complex zeros in this graph.
A. The graph has zeros near 0 and 8.5.
B. There are two real zeros in this graph.
C. There are no real zeros in this graph.
D. The graph has a zero near 35.
E. The graph has only one real zero.
F. There are complex zeros in this graph.
To determine the zeros of the function, we set f(x) = 0 and solve for x.
Given the function f(x) = -2x^2 + 17x + 1,
-2x^2 + 17x + 1 = 0.
We can use the quadratic formula to solve for x:
x = [-b ± √(b^2 - 4ac)] / 2a
In this case, a = -2, b = 17, and c = 1.
Plugging these values into the quadratic formula:
x = [-17 ± √(17^2 - 4*(-2)*1)] / 2*(-2)
x = [-17 ± √(289 + 8)] / -4
x = [-17 ± √297] / -4
x = [-17 ± √(9 * 33)] / -4
x = [-17 ± 3√33] / -4
Therefore, the zeros of the function are:
x = (-17 + 3√33) / 4 and x = (-17 - 3√33) / 4
From these solutions, we see that the function has two real zeros.
Therefore, the correct statements are:
B. There are two real zeros in this graph.
E. The graph has only one real zero.
(Note: Statement E is incorrect based on the analysis of the zeros, so only option B is correct.)
Given the function f(x) = -2x^2 + 17x + 1,
-2x^2 + 17x + 1 = 0.
We can use the quadratic formula to solve for x:
x = [-b ± √(b^2 - 4ac)] / 2a
In this case, a = -2, b = 17, and c = 1.
Plugging these values into the quadratic formula:
x = [-17 ± √(17^2 - 4*(-2)*1)] / 2*(-2)
x = [-17 ± √(289 + 8)] / -4
x = [-17 ± √297] / -4
x = [-17 ± √(9 * 33)] / -4
x = [-17 ± 3√33] / -4
Therefore, the zeros of the function are:
x = (-17 + 3√33) / 4 and x = (-17 - 3√33) / 4
From these solutions, we see that the function has two real zeros.
Therefore, the correct statements are:
B. There are two real zeros in this graph.
E. The graph has only one real zero.
(Note: Statement E is incorrect based on the analysis of the zeros, so only option B is correct.)