Function f is represented by the equation shown.
1 answer:
Answer:
Step-by-step explanation:
A. y-Intercept of ƒ(x)
ƒ(x) = x² - 4x + 3
f(0) = 0² - 4(0) + 3 = 0 – 0 + 3 = 3
The y-intercept of ƒ(x) is (0, 3).
If g(x) opens downwards and has a maximum at y = 3, it's y-intercept is less than (0, 3).
Statement A is TRUE.
B. y-Intercept of g(x)
Statement B is FALSE.
C. Minimum of ƒ(x)
ƒ(x) = x² - 4x + 3
a = 1; b = -4; c = 3
The vertex form of a parabola is
y = a(x - h)² + k
where (h, k) is the vertex of the parabola.
h = -b/(2a) and k = f(h)
h = -b/2a = -(-4)/(2×1 = 2
k = f(2) = 2² - 4×2 + 3 =4 – 8 +3 = -1
The minimum of ƒ(x) is -1. The minimum of ƒ(x) is at (2, -1).
Statement C is FALSE.
D. Minimum of g(x)
g(x) is a downward-opening parabola. It has no minimum.
Statement D is FALSE
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Answer:
1.3 inches
Step-by-step explanation:
1. Determine what you already know in order to set up the equation:
1 inch = 100 miles
<em>x</em> inches = 130 miles
Solving for <em>x</em>
2. Set up the equation so both numerators are the same unit (In this case, both numerators are the mile values and both denominators are the inch values.)
=
3. Cross multiply (Multiply the first fraction's numerator by the second fraction's denominator, and vice versa. It doesn't matter which number is on which side of the = sign.)
100<em>x</em> = 130
4. Divide each side by 100 to isolate the variable.
<em>x</em> = 1.3