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3 years ago

For what value of c will this function have one zero? f(x) = X^2 +c

1 answer:

6 0

X² + c is actually a quadratic function.

And x² + c = 0, it usually has two zeros which are solutions.

But for when c = 0,

x² + c = 0

x² + 0 = 0

x² = 0

Taking the square root of both sides.

x = 0. Here it only has one zero.

So the function x² + c, only has one root for c = 0.

You might be interested in

Find 3 consecutive even integers if their sum decreased by 10 equals -22

Orlov [11]

Three consecutive even integers can be represented by x, (x+2), and (x+4).

(x + (x + 2) + (x + 4)) - 10 = -22 Get rid of the parentheses
x + x + 2 + x + 4 - 10 = -22 Combine like terms (x + x + x) and (2 + 4 - 10)
3x - 4 = -22 Add 4 to both sides
3x = -18 Divide
x = -6
Check you work.

x = -6
x + 2 = -4
x + 4 = -2

(-6 - 4 - 2) - 10 = 22
-12 - 10 = -22

So, your three integers are -6, -4, and -2 .

6 0

3 years ago

1. What types of numbers make up the set of rational numbers?

Ad libitum [116K]

Answer:

Natural Numbers, Whole Numbers, and Integers are rational numbers.

Example: {1, 2, 3, -1, -2, -3}

Numbers with repeating decimals and terminating decimals are also rational.

Example: {2.34343434..., 3.45}

If a square root makes a perfect square, then it is rational.

Example: {√16, √100}

Hope this helps.

8 0

3 years ago

John has a rectangular-shaped field whose length is 62.5 yards and width is 45.3 yards. The area of the field is ________ square

xxMikexx [17]

2831.25 is the area and 215.6 is the perimeter

3 0

3 years ago

PLEASE HELP!! A.S.A.P!!!

tresset_1 [31]

tan A = height /base = 2/3

7 0

3 years ago

Question 5 and 6 please help me

sp2606 [1]

Problem 5

The function is continuous for the given domain $x \ge 6$

This is because y = (-5/6)x+5 is itself continuous, and any interval subset of this function is also continuous. We can plug in any real number that is equal to 6 or larger, and get some y output. If we plugged in x = 6, then we'd get

y = (-5/6)x+5

y = (-5/6)*6 + 5

y = -5+5

y = 0

This is the largest y value possible. Why? Because y = (-5/6)x+5 has a negative slope, so the graph is going downhill as you read it from left to right. As x gets bigger, y gets smaller. The smallest x value allowed in the domain produces the largest y value in the range. There is no smallest y value as the y values keep going down forever.

The range is therefore $y \le 0$

In interval notation, you can write the range as $(-\infty, 0]$ . The square bracket indicates "include this endpoint as part of the range".

======================================================

Problem 6

The function is discrete for this given domain. The domain itself is a discrete list of values. We cannot plug in values between say 0 and 2. We can only substitute one of those values from the list given. Consequently, the y values will also be a list, and not an interval like problem 5 had.

-----------

If you plugged in x = -4, then you should get...

y = (-1/2)*(-4)+2

y = 2+2

y = 4

So the input x = -4 lead the output y = 4

Repeat for x = -2

y = (-1/2)x+2

y = (-1/2)*(-2)+2

y = 1+2

y = 3

and the same for x = 0 as well

y = (-1/2)x+2

y = (-1/2)*0 + 2

y = 0 + 2

y = 2

and x = 2 also

y = (-1/2)x+2

y = (-1/2)*2 + 2

y = -1+2

y = 1

Finally, plug in x = 4

y = (-1/2)x+2

y = (-1/2)*4+2

y = -2+2

y = 0

---------------

If we plugged each of these x values {-4, -2, 0, 2, 4} one at a time into the equation y = (-1/2)x+2, then we get this list of values {4, 3, 2, 1, 0}

Sorting the values from smallest to largest, we have this range {0, 1, 2, 3, 4}

3 0

2 years ago