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emmasim [6.3K]
3 years ago
10

Evaluate the function f (x)= x squared -4x+1 at the given values of the independent variable and simplify.

Mathematics
1 answer:
Ivan3 years ago
8 0
<h3>Given</h3>

... f(x) = x² -4x +1

<h3>Find</h3>

... a) f(-8)

... b) f(x+9)

... c) f(-x)

<h3>Solution</h3>

In each case, put the function argument where x is, then simplify.

a) f(-8) = (-8)² -4(-8) +1 = 64 +32 + 1 = 97

b) f(x+9) = (x+9)² -4(x+9) +1

... = x² +18x +81 -4x -36 +1

... f(x+9) = x² +14x +46

c) f(-x) = (-x)² -4(-x) +1

... f(-x) = x² +4x +1

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part A: expression 1: 6(8m+2)

          expression 2: 6m+12+42m

Part B: 6(m+2+7m)= 6(8m+2)

combine like terms is 6(m+2+7m), so it is 6(2+8m) or 6(8m+2)

6(8m+2)= 6(8m+2)

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3 years ago
A parabolic arch has a height of 25 feet and a span of 40 feet. How high is the arch 8 feet from each side of the center?
Llana [10]

Answer:

The correct option is;

21 ft

Step-by-step explanation:

The equation of the parabolic arc is as follows;

y = a(x - h)² + k

Where the height is 25 ft and the span is 40 ft, the coordinates of the vertex (h, k) is then (20, 25)

We therefore have;

y = a(x - 20)² + 25

Whereby the parabola starts from the origin (0, 0), we have;

0 = a(0 - 20)² + 25

0 = 20²a + 25 → 0 = 400·a + 25

∴a = -25/400 = -1/16

The equation of the parabola is therefore;

y = (-\frac{1}{16})(x-20)^2 + 25

To find the height 8 ft from the center, where the center is at x = 20 we have 8 ft from center = x = 20 - 8 = 12 or x = 20 + 8 = 28

Therefore, plugging the value of x = 12 or 28 in the equation for the parabola gives;

y = (-\frac{1}{16})(12-20)^2 + 25 = (-\frac{1}{16})(-8)^2 + 25 = 21 \ ft.

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