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11 Dec 2020, 01:15
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D
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Difficulty:
25%
(medium)
Question Stats:
80% (01:49) correct
20%
(02:04)
wrong
based on 293
sessions
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The function \(f(x)=(x-\frac{1}{2})^2\) is graphed in the xy-plane. The x-intercept of the graph is (a, 0). The y-intercept of the graph is (0, b). What is the value of \(ab\)?
A. 0.0125
B. 0.1
C. 0.12
D. 0.125
E. 1.25
A. 0.0125
B. 0.1
C. 0.12
D. 0.125
E. 1.25
31 Jan 2025, 00:22
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Rikhraj1
The function \(f(x)=(x-\frac{1}{2})^2\) is graphed in the xy-plane. The x-intercept of the graph is (a, 0). The y-intercept of the graph is (0, b). What is the value of \(ab\)?
A. 0.0125
B. 0.1
C. 0.12
D. 0.125
E. 1.25
Step 1: Find the x-intercept
The x-intercept occurs when f(x) = 0:
(x - 1/2)^2 = 0
x = 1/2
So, the x-intercept is (1/2, 0), meaning a = 1/2.
Step 2: Find the y-intercept
The y-intercept occurs when x = 0:
f(0) = (0 - 1/2)^2 = (-1/2 )^2 = 1/4
So, the y-intercept is (0, 1/4), meaning b = 1/4.
Thus, ab = (1/2) * (1/4) = 1/8 = 0.125.
Answer: D.
General Discussion
11 Dec 2020, 01:31
Kudos
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Given: The function \(f(x)=(x-\frac{1}{2})^2\) is graphed in the xy-plane. The x-intercept of the graph is (a, 0). The y-intercept of the graph is (0, b).
Asked: What is the value of \(ab\)?
x - intercept: -
At x = a = 1/2 ; y = 0
a = 1/2
y - intercept: -
x = 0
y = b = 1/2ˆ2 = 1/4
b = 1/4
ab = (1/2) * (1/4) = 1/8 = 0.125
IMO D
Asked: What is the value of \(ab\)?
x - intercept: -
At x = a = 1/2 ; y = 0
a = 1/2
y - intercept: -
x = 0
y = b = 1/2ˆ2 = 1/4
b = 1/4
ab = (1/2) * (1/4) = 1/8 = 0.125
IMO D
